a second wronskian formulation of the boussinesq equation a wronskian formulation leading to rational solutions is presented for the boussinesq equation it involves third order linear partial differential equations whose representative systems are systematically solved the resulting solutions formulas provide a direct but powerful approach for constructing rational solutions positon solutions and complexiton solutions to the boussinesq equation various examples of exact solutions of those three kinds are computed the newly presented wronskian formulation is different from the one previously presented by li et al which does not yield rational solutions

einstein maxwell solitons the application of the inverse scattering method to the einstein maxwell equations for stationary axisymmetric exterior fields leads the authors to an explicit formula for the ernst and electromagnetic potentials of new exact solutions generated from an arbitrary seed solution

darboux transforms deep reductions and solitons explicit formalisms for deep reductions of matrix differential equations and darboux covariance properties are presented the matrix 2 2 spectral problem of the second order is considered this problem with the reduction constraints being imposed on the potentials is the first equation of the lax representation of the hirota satsuma system 1981 the two reduction cases are treated with the help of the bilinear delta forms the covariance of these forms with respect to the darboux transforms under restrictions gives rise to explicit formulas of n soliton solutions in particular the two parameter soliton solutions of the hirota satsuma system are obtained the specific feature of such solutions evolution is that the singularity appears in some parameter region the yajima oikawa system 1976 is given as an example of the technique application to a 3 3 spectral problem

multiple travelling wave solutions of nonlinear evolution equations using a unified algebraic method a new direct and unified algebraic method for constructing multiple travelling wave solutions of general nonlinear evolution equations is presented and implemented in a computer algebraic system compared with most of the existing tanh methods the jacobi elliptic function method or other sophisticated methods the proposed method not only gives new and more general solutions but also provides a guideline to classify the various types of the travelling wave solutions according to the values of some parameters the solutions obtained in this paper include a kink shaped and bell shaped soliton solutions b rational solutions c triangular periodic solutions and d jacobi and weierstrass doubly periodic wave solutions among them the jacobi elliptic periodic wave solutions exactly degenerate to the soliton solutions at a certain limit condition the efficiency of the method can be demonstrated on a large variety of nonlinear evolution equations such as those considered in this paper kdv mkdv ito s fifth mkdv hirota nizhnik novikov veselov broer kaup generalized coupled hirota satsuma coupled schrodinger kdv 2 1 dimensional dispersive long wave 2 1 dimensional davey stewartson equations in addition as an illustrative sample the properties of the soliton solutions and jacobi doubly periodic solutions for the hirota equation are shown by some figures the links among our proposed method the tanh method extended tanh method and the jacobi elliptic function method are clarified generally

analytical positon negaton and complexiton solutions for the coupled modified kdv system new analytical positon negaton and complexiton solutions for the coupled modified kdv system are constructed by means of the darboux transformation with a constant seed solution and given out both analytically and graphically

inapproximability of maximal strip recovery in comparative genomics the first step of sequence analysis is usually to decompose two or more genomes into syntenic blocks that are segments of homologous chromosomes for the reliable recovery of syntenic blocks noise and ambiguities in the genomic maps need to be removed first maximal strip recovery msr is an optimization problem proposed by zheng zhu and sankoff for reliably recovering syntenic blocks from genomic maps in the midst of noise and ambiguities given d genomic maps as sequences of gene markers the objective of msr d is to find d subsequences one subsequence of each genomic map such that the total length of syntenic blocks in these subsequences is maximized for any constant d 2 a polynomial time 2d approximation for msr d was previously known in this paper we show that for any d 2 msr d is apx hard even for the most basic version of the problem in which all gene markers are distinct and appear in positive orientation in each genomic map moreover we provide the first explicit lower bounds on approximating msr d for all d 2 in particular we show that msr d is np hard to approximate within w d logd from the other direction we show that the previous 2d approximation for msr d can be optimized into a polynomial time algorithm even if d is not a constant but is part of the input we then extend our inapproximability results to several related problems including cmsr d d gap msr d and d gap cmsr d

residual based methods for fluid loaded beams abstract in this paper residual based modifications to standard finite element approximations for structural acoustics are developed and analyzed results for symmetric residual based modifications for the coupled problem are presented the accuracy of symmetric and unsymmetric methods is determined in a two dimensional setting a symmetric form of the residual based modification results in lower computational costs than the other methods the inclusion of new fluid structure coupling and fluid stiffness terms arising from the consistent integration into the coupled formulation of residual modifications to the structural equations is shown to dramatically decrease the l 2 error

analytic solutions darboux transformation operators and supersymmetry for a generalized one dimensional time dependent schrodinger equation abstract in this paper analytically investigated is a generalized one dimensional time dependent schrodinger equation using darboux transformation operator technique we construct the first order darboux transformation and the real valued condition of transformed potential for the generalized schrodinger equation to prove the equivalence of the supersymmetry formalism and the darboux transformation we investigate the relationship among first order darboux transformation supersymmetry and factorization of the corresponding effective mass hamiltonian furthermore the nth order darboux transformations are constructed by means of different method finally by using darboux transformation some analytical solutions are generated in a recursive manner for some examples of the schrodinger equation

some new integrable nonlinear evolution equations and darboux transformation two classes of new nonlinear evolution equations are derived with the aid of a 4 4 matrix spectral problem with three potentials a darboux transformation for the first nontrivial nonlinear evolution equation is given based on the gauge transformation between the corresponding 4 4 matrix spectral problems as an application of the darboux transformation some explicit solutions of the nontrivially nonlinear evolution equation are obtained

interactions among periodic waves and solitary waves for a higher dimensional system the general variable separated approach is successfully extended to the 2 1 dimensional physical model and we obtain a universal formula involving arbitrary number of variable separated functions because of the existence of the arbitrary functions in the universal formula many new types of structures of periodic waves for example the periodic periodic interaction waves periodic kink interaction waves periodic peakon interaction waves periodic compacton interaction waves periodic foldon interaction waves etc are investigated both analytically and graphically some novel features or interesting behaviours are revealed

solitary wave and periodic wave solutions for the thermally forced gravity waves in atmosphere by introducing a new transformation a new direct and unified algebraic method for constructing multiple travelling wave solutions of general nonlinear evolution equations is presented and implemented in a computer algebraic system which extends fan s direct algebraic method to the case when r 4 the solutions of a first order nonlinear ordinary differential equation with a higher degree nonlinear term and fan s direct algebraic method of obtaining exact solutions to nonlinear partial differential equations are applied to the combined kdv mkdv gkdv equation which is derived from a simple incompressible non hydrostatic boussinesq equation with the influence of thermal forcing and is applied to investigate internal gravity waves in the atmosphere as a result by taking advantage of the new first order nonlinear ordinary differential equation with a fifth degree nonlinear term and an eighth degree nonlinear term periodic wave solutions associated with the jacobin elliptic function and the bell and kink profile solitary wave solutions are obtained under the effect of thermal forcing most importantly the mechanism of propagation and generation of the periodic waves and the solitary waves is analysed in detail according to the values of the heating parameter which show that the effect of heating in atmosphere helps to excite westerly or easterly propagating periodic internal gravity waves and internal solitary waves in atmosphere which are affected by the local excitation structures in atmosphere in addition as an illustrative sample the properties of the solitary wave solution and jacobin periodic solution are shown by some figures under the consideration of heating interaction

complex wave number dispersion analysis of galerkin and galerkin least squares methods for fluid loaded plates abstract the technique of complex wave number dispersion analysis is used to examine the accuracy of discretized systems in the representation of wave propagation phenomena this technique was applied to study finite element approximations to in vacuo and fluid loaded plates considering discretizations of kirchhoff and reissner mindlin plate theories coupled to an acoustic medium the allowed evanescent waves in the finite element approximation of the in vacuo plate are obtained and compared with theory the finite element dispersion relation for the coupled plate fluid system is derived results for the galerkin structural approximation coupled to galerkin and galerkin least squares gls fluid formulations are presented quantitative errors are reported and the significance of these errors in view of an analytical solution to the problem is given

complexity of approximating bounded variants of optimization problems we study low degree graph problems such as maximum independent set and minimum vertex cover the goal is to improve approximation lower bounds for them and for a number of related problems like max b set packing min b set cover and max b dimensional matching b 3 we prove for example that it is np hard to achieve an approximation factor of 95 94 for max 3 dm and a factor of 48 47 for max 4 dm in both cases the hardness result applies even to instances with exactly two occurrences of each element

link between solitary waves and projective riccati equations many solitary wave solutions of nonlinear partial differential equations can be written as a polynomial in two elementary functions which satisfy a projective hence linearizable riccati system from that property the authors deduce a method for building these solutions by determining only a finite number of coefficients this method is much shorter and obtains more solutions than the one which consists of summing a perturbation series built from exponential solutions of the linearized equation they handle several examples for the henon heiles hamiltonian system they obtain several exact solutions one of them defines a new solitary wave solution for a coupled system of boussinesq and nonlinear schrodinger equations for a third order dispersive equation with two monomial nonlinearities they isolate all cases where the general solution is single valued

numerical integration of a coupled korteweg de vries system abstract we introduce a numerical method for general coupled korteweg de vries systems the scheme is valid for solving cauchy problems for an arbitrary number of equations with arbitrary constant coefficients the numerical scheme takes its legality by proving its stability and convergence which gives the conditions and the appropriate choice of the grid sizes the method is applied to the hirota satsuma hs system and compared with its known explicit solution investigating the influence of initial conditions and grid sizes on accuracy we also illustrate the method to show the effects of constants with a transition to nonintegrable cases

stabilized finite element methods for steady advection diffusion with production abstract finite element methods for solving equations of steady advection diffusion with production are constructed employing a linear source to model production the galerkin method requires relatively fine meshes to retain an acceptable degree of accuracy for wide ranges of values of the physical coefficients numerous criteria for improved accuracy via galerkin least squares are proposed and examined in the entire parameter space of these several provide the lowest error in nodal amplification factors each in a certain range of ratios of physical coefficients guidelines for required mesh resolutions are presented for galerkin and galerkin least squares showing that in large parts of the parameter space substantial savings may be obtained by employing galerkin least squares galerkin least squares gradient least squares a new variation of the galerkin method is designed to provide exact nodal amplification factors offering accurate solutions at any resolution numerical tests validate these conclusions

reduction of dispersionless coupled korteweg de vries equations to the euler darboux equation a quasilinear hyperbolic system of two first order equations is introduced the system is linearized by means of the hodograph transformation combined with riemann s method of characteristics in the process of linearization the main step is to explicitly express the characteristic velocities in terms of the riemann invariants the procedure is shown to be performed by quadrature only for specific combinations of the parameters in the system we then apply the method developed here to the dispersionless versions of the typical coupled korteweg de vries ckdv equations including the broer kaup ito hirota satsuma and bogoyavlenskii equations and show that these equations are transformed into the classical euler darboux equation a more general quasilinear system of equations is also considered with application to the dispersionless ckdv equations for the jaulent miodek and nutku oguz equations

darboux transformation and soliton like solutions for the gerdjikov ivanov equation an explicit n fold darboux transformation with multiparameters for a kind of coupled derivative nonlinear schrodinger equation is constructed with the help of a gauge transformation of a spectral problem as a reduction a darboux transformation of the gerdjikov ivanov equation is obtained furthermore the explicit soliton like solutions of the gerdjikov ivanov equation are given by applying its darboux transformation

some apx completeness results for cubic graphs four fundamental graph problems minimum vertex cover maximum independent set minimum dominating set and maximum cut are shown to be apx complete even for cubic graphs therefore unless p np these problems do not admit any polynomial time approximation scheme on input graphs of degree bounded by three

a galerkin least squares finite element method for the two dimensional helmholtz equation in this paper a galerkin least squares gls finite element method in which residuals in least squares form are added to the standard galerkin variational equation is developed to solve the helmholtz equation in two dimensions an important feature of gls methods is the introduction of a local mesh parameter that may be designed to provide accurate solutions with relatively coarse meshes previous work has accomplished this for the one dimensional helmholtz equation using dispersion analysis in this paper the selection of the gls mesh parameter for two dimensions is considered and leads to elements that exhibit improved phase accuracy for any given direction of wave propagation an optimal gls mesh parameter is determined using two dimensional fourier analysis in general problems the direction of wave propagation will not be known a priori in this case an optimal gls parameter is found which reduces phase error for all possible wave vector orientations over elements the optimal gls parameters are derived for both consistent and lumped mass approximations several numerical examples are given and the results compared with those obtained from the galerkin method the extension of gls to higher order quadratic interpolations is also presented

generalized tanh method with symbolic computation and generalized shallow water wave equation abstract we report that symbolic computation with the generalized tanh method leads to new soliton like solutions for a 2 1 dimensional generalization of the shallow water wave equations

design of galerkin generalized least squares methods for timoshenko beams abstract a class of finite element methods the galerkin generalized least squares methods are developed and applied to model the steady state response of timoshenko beams an optimal method is designed using a linear interpolation of the response such that there is zero finite element dispersion error the classical method of selective reduced integration and a modified version of selective reduced integration with mass lumping are shown to fall under the galerkin generalized least squares framework numerical experiments in wave propagation demonstrate the dramatic superiority of the new optimal method over the standard approaches the goal of the new methods is to decrease the computational burden required to achieve a desired accurcy level at a particular frequency thereby enabling larger scale higher frequency computations for a given platform

on the parameterized complexity of some optimization problems related to multiple interval graphs we show that for any constant t 2 k independent set and k dominating set in t track interval graphs are w 1 hard this settles an open question recently raised by fellows hermelin rosamond and vialette we also give an fpt algorithm for k clique in t interval graphs parameterized by both k and t with running time max t o k 2 o k l o g k poly n where n is the number of vertices in the graph this slightly improves the previous fpt algorithm by fellows hermelin rosamond and vialette finally we use the w 1 hardness of k independent set in t track interval graphs to obtain the first parameterized intractability result for a recent bioinformatics problem called maximal strip recovery msr we show that msr d is w 1 hard for any constant d 4 when the parameter is either the total length of the strips or the total number of adjacencies in the strips or the number of strips in the solution

a generalized hirota satsuma coupled kdv system darboux transformations and reductions a darboux transformation is constructed for the generalized hirota satsuma coupled kdv system and the result is compared with the recent work of geng and his collaborators x g geng et al phys rev e 79 056602 2009 and x g geng and g l he j math phys 51 033514 2010 it is shown that our darboux transformation may be applied to three interesting reductions of the general system in addition the iteration of this darboux transformation is worked out and some solutions to the associated systems are obtained

a generalized hirota equation in 2 1 dimensions using an asymptotically exact reduction method based on fourier expansion and spatiotemporal rescaling a new integrable and nonlinear partial differential equation pde in 2 1 dimensions is obtained starting from the kadomtsev petviashvili equation we apply the reduction technique to the lax pair of the kadomtsev petviashvili equation and demonstrate the integrability property of the new equation because we obtain the corresponding lax pair the new equation reduces to the hirota equation in the 1 1 dimensional limit

algebraic construction of the darboux matrix revisited we present algebraic construction of darboux matrices for 1 1 dimensional integrable systems of nonlinear partial differential equations with a special stress on the nonisospectral case we discuss different approaches to the darboux backlund transformation based on different dependences of the darboux matrix polynomial sum of partial fractions or the transfer matrix form we derive symmetric n soliton formulae in the general case the matrix spectral parameter and dressing actions in loop groups are also discussed we describe reductions to twisted loop groups unitary reductions the matrix lax pair for the kdv equation and reductions of chiral models harmonic maps to su n and to grassmann spaces we show that in the kdv case the nilpotent darboux matrix generates the binary darboux transformation the paper is intended as a review of known results usually presented in a novel context but some new results are included as well e g general compact formulae for n soliton surfaces and linear and bilinear constraints on the nonisospectral lax pair matrices which are preserved by darboux transformations

symmetry algebras of the potential nizhnik novikov veselov model two sets of generalized symmetries of the potential nizhnik novikov veselov equation are given in a simple formula by developing a generalized formal series method for searching symmetries of one type of generalized partial differential equations these two sets of symmetries constitute an infinite dimensional lie algebra which contains three types of virasoro algebras and three w type algebras as its special cases

darboux transformation and explicit solutions for the satsuma hirota coupled equation abstract a darboux transformation for the satsuma hirota coupled equation is obtained with the help of the gauge transformation between the lax pairs as an application of the darboux transformation we give some new explicit solutions including rational solutions soliton solutions and periodic solutions and others of the satsuma hirota coupled equation

tractability and approximability of maximal strip recovery an essential task in comparative genomics is to decompose two or more genomes into synteny blocks that are segments of chromosomes with similar contents given a set of d genomic maps each containing the same n markers without duplicates the problem maximal strip recovery msr aims at finding a decomposition of the genomic maps into synteny blocks strips of the maximum total length by deleting the minimum number k n of markers which are probably noise and ambiguities in this paper we present a collection of new or improved fpt and approximation algorithms for msr and its variants our main results include a 2 o d d poly nd time fpt algorithm for d gap msr d a 2 36 kpoly nd time fpt algorithm for both cmsr d and d gap cmsr d and a d 1 5 approximation algorithm for both cmsr d and d gap cmsr d

constructing of new exact solutions to the gkdv mkdv equation with any order nonlinear terms by g g expansion method abstract the g g expansion method is introduced to construct more general exact travelling wave solutions to the generalized kdv mkdv equation with any order nonlinear terms as a result hyperbolic function solution trigonometric function solution and rational solution with parameters are obtained when the parameters take up special values the solitary waves are also derived from the travelling wave solutions the g g expansion method presents a wider applicability for handling nonlinear wave equations

classification of polynomial integrable systems of mixed scalar and vector evolution equations i we perform a classification of integrable systems of mixed scalar and vector evolution equations with respect to higher symmetries we consider polynomial systems that are homogeneous under a suitable weighting of variables this paper deals with the kdv weighting the burgers or potential kdv or modified kdv weighting the ibragimov shabat weighting and two unfamiliar weightings the case of other weightings will be studied in a subsequent paper making an ansatz for undetermined coefficients and using a computer package for solving bilinear algebraic systems we give the complete lists of second order systems with a third order or a fourth order symmetry and third order systems with a fifth order symmetry for all but a few systems in the lists we show that the system or at least a subsystem of it admits either a lax representation or a linearizing transformation a thorough comparison with recent work of foursov and olver is made

acoustic radiation from an insonified elastic plate with a line discontinuity this paper deals with the development of analytic models for the prediction of the acoustic radiated field from an infinite elastic plate with a single line force and line moment impedance discontinuity due to an incident plane acoustic wave the solution is in the form of a fourier integral with a kernel having ten poles the integral is evaluated by three methods the first uses the steepest descent path sdp method leading to a solution that decays as 1 k0r 1 2 the second method used conformal transformations and the modified saddle point msp method where all ten poles of the integrand are factored out this second method yields a solution that has complementary error functions and an asymptotic series in k0r the third method employs a transformation of the integrand to effect an efficient and fastly convergent numerical integration algorithm in general the msp asymptotic series solution and the numerical integration yielded numerically identical results however while the sdp solution pre

complexiton solutions to integrable equations abstract complexiton solutions or complexitons for short are exact solutions newly introduced to integrable equations are newly introduced starting with the solution classification for a linear differential equation the korteweg de vries equation and the toda lattice equation are considered as examples to exhibit complexiton structures of nonlinear integrable equations the crucial step in the solution process is to apply the wronskian and casoratian techniques for hirota s bilinear equations correspondence between complexitons of the korteweg de vries equation and complexitons of the toda lattice equation is provided

new rational solitary wave solutions of 2 1 dimensional burgers equation abstract based on the computer symbolic system maple and the rational solitary wave solutions and rational periodic solutions obtained by others previously we present a new direct ansatz in terms of the hyperbolic functions and periodic function to solve the nonlinear evolution equations that is to say we assume the equations have the solution in the following form u i a i 0 j 1 n i g j 1 a i j f b i j g c i j h d i j r where f tanh sech a b tanh c sech 2 g sech a b tanh c sech 2 h sech 2 a b tanh c sech 2 r tanh a b tanh c sech 2 and a 2 b 2 c 2 0 compared with the solutions obtained by the existing tanh methods riccati equation method and all kinds of their improved methods the solutions obtained by the proposed direct method not only include some obtained solutions but also include some new and general rational solutions and we choose the 2 1 dimensional burgers equation to illustrate the key step as a result we obtain abundant families of rational solitary wave solutions and rational periodic solutions furthermore the direct method is proved to be efficient

the variational theory of complex rays a predictive tool for medium frequency vibrations abstract today the main numerical modeling techniques for the analysis of medium frequency vibrations are all based on finite element or boundary element approaches in order to represent small wavelength phenomena in complex structures such as car chassis satellites or ships these techniques require a huge number of degrees of freedom at least seven elements per wavelength are required to represent oscillating solutions in addition the solution obtained is highly sensitive to material properties and boundary conditions the use of high frequency approaches such as the statistical energy analysis sea or any of its improvements does not appear to be suitable for medium frequency vibrations the vibrational behavior becomes too smooth and in general the coupling loss factor cannot be calculated in a predictive way in this paper a new and multiscale approach to the calculation of the vibrations of elastic structures in the medium frequency range called the variational theory of complex rays is presented the feasibility and effectiveness of the method are demonstrated for structures made of plate assemblies several 3d examples are analyzed and compared to the results from a classical finite element approach and from a sea code this comparison shows that our method is able to predict the effective quantities at a very low numerical cost

a rational generalization of fan s method and its application to generalized shallow water wave equations in this paper we employ a rational expansion to generalize fan s method for exact travelling wave solutions for nonlinear partial differential equations pdes to verify the reliability of the proposed method the generalized shallow water wave gsww equation has been investigated as an example kinds of new exact travelling wave solutions of a rational form have been obtained this indicates that the proposed method provides a more general result for exact solution of nonlinear equations

delta dressing and exact solutions for the 2 1 dimensional harry dym equation exact implicit solutions with functional parameters of the 2 1 dimensional harry dym hd equation are constructed by the delta dressing method the interrelation between the hd and modified kadomtsev petviashvili mkp equations is established within the framework of the delta dressing method knowledge of the mkp eigenfunctions allows the solutions of the 2 1 dimensional hd equation to be represented in a simple parametric form

scheduling split intervals we consider the problem of scheduling jobs that are given as groups of nonintersecting segments on the real line each job j j is associated with an interval i j which consists of up to t segments for some t geq 1 and a weight profit w j two jobs are in conflict if their intervals intersect such jobs show up in a wide range of applications including the transmission of continuous media data allocation of linear resources e g bandwidth in linear processor arrays and computational biology geometry the objective is to schedule a subset of nonconflicting jobs of maximum total weight our problem can be formulated as the problem of finding a maximum weight independent set in a t interval graph the special case of t 1 is an ordinary interval graph we show that for t geq 2 this problem is apx hard even for highly restricted instances our main result is a 2t approximation algorithm for general instances this is based on a novel fractional version of the local ratio technique one implication of this result is the first constant factor approximation for nonoverlapping alignment of genomic sequences we also derive a bicriteria polynomial time approximation scheme for a restricted subclass of t interval graphs

nonlocal symmetries of the hirota satsuma coupled korteweg de vries system and their applications exact interaction solutions and integrable hierarchy the nonlocal symmetry is derived from the known darboux transformation dt of the hirota satsuma coupled korteweg de vries hs ckdv system and infinitely many nonlocal symmetries are given by introducing the internal parameters by extending the hs ckdv system to an auxiliary system with five dependent variables the prolongation is found to localize the so called seed nonlocal symmetry related to the dt by applying the general lie point symmetry method to this enlarged system we obtain two main results a new type of finite symmetry transformation is derived which is different from the initial dt and can generate new solutions from old ones some novel exact interaction solutions among solitons and other complicated waves including periodic cnoidal waves and painleve waves are computed through similarity reductions in addition two kinds of new integrable models are proposed from the obtained nonlocal symmetry the negative hs ckdv hierarchy by introducing the internal parameters the integrable models both in lower and higher dimensions by restricting the symmetry constraints

complexiton solutions of the toda lattice equation a set of coupled conditions consisting of differential difference equations is presented for casorati determinants to solve the toda lattice equation one class of the resulting conditions leads to an approach for constructing complexiton solutions to the toda lattice equation through the casoratian formulation an analysis is made for solving the resulting system of differential difference equations thereby providing the general solution yielding eigenfunctions required for forming complexitons moreover a feasible way is presented to compute the required eigenfunctions along with examples of real complexitons of lower order

interactions among periodic waves and solitary waves of the n 1 dimensional sine gordon field exact solutions of the n 1 dimensional sine gordon field equation are studied with help of those of the cubic nonlinear klein gordon fields the mapping relations among the sine gordon field equation and the cubic nonlinear klein gordon fields are pure algebraic by solving the cubic nonlinear klein gordon equations many new types of exact explicit solutions such as the periodic periodic interaction waves periodic kink interaction waves periodic perturbed snake shape solitary waves etc are displayed both analytically and graphically

an improved linear kernel for complementary maximal strip recovery simpler and smaller abstract we study the complementary maximal strip recovery problem cmsr where the given are two strings s 1 and s 2 of distinct letters each of which appears either in the positive form or the negative form the question is whether there are k letters whose deletion results in two matched strings string s 1 matches string s 2 if there are partitions of s 1 and s 2 such that each component of the partitions contains at least two letters and moreover for each component s 1 i of the partition of s 1 there is a unique component s 2 j in the partition of s 2 which is either equal to s 1 i or can be obtained from s 1 i by firstly reversing the order of the letters and then negating the letters the cmsr problem is known to be np hard and fixed parameter tractable with respect to k in particular a linear kernel of size 74 k 4 was developed based on 8 reduction rules very recently by imposing 3 new reduction rules to the previous kernelization the linear kernel has been improved to 58k we aim to simplify the kernelization yet obtain an improved kernel in particular we study 7 reduction rules which lead to a linear kernel of size 42 k 24

remarks on a system of coupled nonlinear wave equations it is shown that a generalized system of coupled kdv mkdv equation exhibits solitary wave solutions it has been shown that an increase in nonlinearity in one variable in a particular fashion does not affect the existence of solitary wave solutions the periodic traveling wave solutions of the system have also been investigated

constructing of exact solutions to the kdv and burgers equations with power law nonlinearity by the extended g g expansion method abstract the extended g g expansion method is introduced to construct more general exact traveling wave solutions to the kdv and burgers equations with any order nonlinear terms the traveling wave solutions are expressed by the hyperbolic functions the trigonometric functions and the rational functions when the parameters take up special values new solitary periodic and complex solutions are also derived from the traveling wave solutions

on the hardness of approximating minimum vertex cover we prove the minimum vertex cover problem to be np hard to approximate to within a factor of 1 3606 extending on previous pcp and hardness of approximation technique to that end one needs to develop a new proof framework and to borrow and extend ideas from several fields

multiple kink solutions and multiple singular kink solutions for the 2 1 dimensional burgers equations abstract in this work we study the 2 1 dimensional painleve integrable burgers equation multiple kink solutions and multiple singular kink solutions are formally derived for this equation the analysis depends mainly on the hirota s bilinear method

a family of completely integrable multi hamiltonian systems explicitly related to some celebrated equations by introducing a spectral problem with an arbitrary parameter we derive a kaup newell type hierarchy of nonlinear evolution equations which is explicitly related to many important equations such as the kundu equation the kaup newell kn equation the chen lee liu cll equation the gerdjikov ivanov gi equation the burgers equation the modified korteweg devries mkdv equation and the sharma tasso olver equation it is shown that the hierarchy is integrable in liouville s sense and possesses multi hamiltonian structure under the bargann constraint between the potentials and the eigenfunctions the spectral problem is nonlinearized as a finite dimensional completely integrable hamiltonian system the involutive representation of the solutions for the kaup newell type hierarchy is also presented in addition an n fold darboux transformation of the kundu equation is constructed with the help of its lax pairs and a reduction technique according to the darboux transformation the solutions of the ku

extension of the variational theory of complex rays to shells for medium frequency vibrations a new approach to the calculation of vibrations of weakly damped elastic structures in the medium frequency range called the variational theory of complex rays vtcr is being developed here the extension of this theory to shells of relatively small curvature is considered numerical examples of structures made of plates and shells demonstrate the capabilities of the vtcr

galerkin generalized least squares finite element methods for time harmonic structural acoustics galerkin generalized least squares ggls finite element methods are developed and implemented for modeling the response of fluid loaded structures a general formalism for the application of this methodology to problems in structural acoustics the vibration of an elastic structure in contact with an acoustic medium is presented a consistent approach for the development and implementation of the design parameters inherent to the ggls methods for coupled problems is given this general methodology is then applied to an exterior problem of a fluid loaded reissner mindlin plate complex wave number dispersion analysis and numerical experiments demonstrate clearly the reduction of storage requirements and solution time of the new ggls methods over standard discretization techniques

lie transformations nonlinear evolution equations and painleve forms we present the results of a systematic investigation of invariance properties of a large class of nonlinear evolution equations under a one parameter continuous lie group of transformations it is shown that in general the corresponding invariant variables the subclass of which is the usual similarity variables lead to ordinary differential equations of painleve type in the case of inverse scattering transform solvable equations as conjectured by ablowitz ramani and segur this is found to be also true for certain higher spatial dimensional versions such as the kadomtsev petviashivilli two dimensional sine gordon and ernst equations for the nonsolvable equations considered here this invariance study leads to ordinary differential equations with movable critical points

elementary and binary darboux transformations at rings for a given idempotent p and some element from a differential associative ring we introduce gauge transformation p with the spectral parameter that leaves some linear operators form invariant the explicit form of the is derived for the generalized zakharov shabat problem the maps that factorize darboux transformations are referred to as elementary ones binary transformations that correspond to the iteration of elementary maps with the special choice of solutions of the direct and conjugate problems are introduced and widen the potential reductions set we show an infinitesimal version of iterated transforms the spectral operator and soliton theories applications are outlined the nonabelian n wave interaction equation modification with additional linear terms its zero curvature representation soliton solutions and their stability with respect to infinitesimal deformations are studied

on the complexity of unsigned translocation distance translocation is one of the basic operations for genome rearrangement translocation distance is the minimum number of translocations required to transform one genome into the other in this paper we show that computing the translocation distance for unsigned genomes is np hard moreover we show that approximating the translocation distance for unsigned genomes within ratio 1 00017 is np hard

new analytical positon negaton and complexiton solutions of a coupled kdv mkdv system new positon negaton and complexiton solutions of a coupled kdv mkdv system are constructed directly from zero seed solution by means of darboux transformation these new exact solutions are all analytical with different spectral parameters and constants selection

complexitons of the modified kdv equation by darboux transformation abstract darboux transformation dt a comprehensive approach to construct the explicit solutions of the nonlinear evolutionary equation is applied to construct the new complexiton solution of the negative mkdv equation we find that the complexiton solution is related to the single complex spectral parameter and that it is completely different from the breather solution for the positive mkdv equation consequently we generalize the concept of complexiton of the kdv equation to the mkdv equation in addition the relationship of the spectral parameter and the known solutions of the mkdv equation is clarified and the multi complexiton solution multi complexiton positon multi complexiton negaton and multi complexiton soliton solutions are obtained in the uniform manner by dt the interaction of complexiton and soliton is also discussed in detail it is shown that the new complexiton and soliton remain unchanged except for phase shifts after their interaction at the same time the superreflectionless property of one positon potential for the mkdv equation is shown in detail

painleve property soliton like solutions and complexitons for a coupled variable coefficient modified korteweg de vries system in a two layer fluid model abstract as a model derived from a two layer fluid system which describes the atmospheric and oceanic phenomena a coupled variable coefficient modified korteweg de vries system is concerned in this paper with the help of symbolic computation its integrability in the painleve sense is investigated furthermore hirota s bilinear method is employed to construct the bilinear forms through the dependent variable transformations and soliton like solutions and complexitons are derived finally effects of variable coefficients are discussed graphically and it is concluded that the variable coefficients control the propagation trajectories of solitons and complexitons