a block triple relaxation time lattice boltzmann model for nonlinear anisotropic convection diffusion equations abstract a block triple relaxation time b trirt lattice boltzmann model for general nonlinear anisotropic convection diffusion equations nacdes is proposed and the chapman enskog analysis shows that the present b trirt model can recover the nacdes correctly there are some striking features of the present b trirt model firstly the relaxation matrix of b trirt model is partitioned into three relaxation parameter blocks rather than a diagonal matrix in general multiple relaxation time mrt model secondly based on the analysis of half way bounce back hbb scheme for dirichlet boundary conditions we obtain an expression to determine the relaxation parameters thirdly the anisotropic diffusion tensor can be recovered by the relaxation parameter block that corresponds to the first order moment of non equilibrium distribution function a number of simulations of isotropic and anisotropic convection diffusion equations are conducted to validate the present b trirt model the results indicate that the present model has a second order accuracy in space and is also more accurate and more stable than some available lattice boltzmann models

the painleve property for partial differential equations in this paper we define the painleve property for partial differential equations and show how it determines in a remarkably simple manner the integrability the backlund transforms the linearizing transforms and the lax pairs of three well known partial differential equations burgers equation kdv equation and the modified kdv equation this indicates that the painleve property may provide a unified description of integrable behavior in dynamical systems ordinary and partial differential equations while at the same time providing an efficient method for determining the integrability of particular systems

sensitivity analysis of solutions to optimization problems in hilbert spaces with applications to optimal control and estimation abstract this research provides sufficient conditions for lipschitz continuity and directional differentiability of the solutions and the lagrange multipliers of constraint nonlinear programming problems in hilbert spaces the abstract results are applied to problems in optimal control and parameter estimation

distinct variants of the kdv equation with compact and noncompact structures in this paper we examine three distinct variants of the generalized kdv equation both the compact and the noncompact structures are treated for these variants we also emphasize the different physical structures of the two classes the focusing branch and the defocusing branch

a generalized auxiliary equation method and its application to the 2 1 dimensional kdv equations abstract in this paper a generalized auxiliary equation method is proposed to construct more general exact solutions of nonlinear partial differential equations as an application of the method the 2 1 dimensional korteweg de vries equations are considered as a result many new and more general non travelling wave and coefficient function solutions are obtained including soliton like solutions trigonometric function solutions exponential solutions and rational solutions

identification of parabolic distributed parameter systems by regularization with differential operators abstract the theory of identification of variable coefficients in parabolic distributed parameter systems by regularization is extended to the case in which the stabilizing functional is the norm of a differential operator stability and convergence of the method are proved a detailed computational evaluation of the approach is presented via the estimation of a spatially varying conductivity in the two dimensional heat equation

the calculation of novel class of solutions of a non linear fourth order evolution equation by the weierstras transform method abstract in this paper the weierstras transform method is applied to a non linear partial differential equation npde of fourth order to obtain new exact class of solutions in terms of the weierstras elliptic function g 2 g 3 the major aspect of this paper however is the fact that we are able to calculate distinctive class of solutions of a less studied non linear evolution equation explicitly given by u tt u xxxt 3 u xx u xt 0 the derived class of solutions cannot be found in the current literature more precisely the mathematical structure of these class of solutions are quite different from those derived by classical ansatz methods in other words using this special algebraic procedure the solution manifold is augmented to further class of solutions including special functions they are connected in a complicate way and allow a more general representation as found in previous time simultaneously we would like to stress the necessity of such sophisticated methods since a general theory of npdes does not exist in addition this paper is a logical completion of our recent studies where we have applied successfully the weierstras transform method to the important kdv mkdv equation

a generalized auxiliary equation method and its application to 2 1 dimensional asymmetric nizhnik novikov vesselov equations a generalized auxiliary equation method is proposed to construct more general exact solutions of nonlinear partial differential equations with the aid of symbolic computation we choose the 2 1 dimensional asymmetric nizhnik novikov vesselov equations to illustrate the validity and advantages of the method as a result many new and more general exact non travelling wave and coefficient function solutions are obtained including soliton like solutions triangular like solitions single and combined non degenerate jacobi elliptic doubly like periodic solutions and weierstrass elliptic doubly like periodic solutions

an approximation theory for the identification of nonlinear distributed parameter systems an abstract approximation framework for the identification of nonlinear distributed parameter systems is developed inverse problems for nonlinear systems governed by strongly maximal monotone operators satisfying a mild continuous dependence condition with respect to the unknown parameters to be identified are treated convergence of galerkin approximations and the corresponding solutions of finite dimensional approximating identification problems to a solution of the original infinite dimensional identification problem is demonstrated using the theory of nonlinear evolution systems and a nonlinear analogue of the trotter kato approximation result for semigroups of bounded linear operators the nonlinear theory developed here is shown to subsume an existing linear theory as a special case it is also shown to be applicable to a broad class of nonlinear elliptic operators and the corresponding nonlinear parabolic partial differential equations to which they lead an application of the theory to a quas

a quasi newton method for estimating the parameter in a nonlinear hyperbolic system a quasi newton method qnm in infinite dimensional spaces for estimating parameters involved in distributed parameter systems is presented in this paper next the global convergence of a sequence generated by the algorithm qnm is also proved we apply the algorithm qnm to an identification problem of a distributed parameter system governed by a nonlinear hyperbolic partial differential equation

identification of distributed parameter systems with pointwise constraints on the parameters abstract the problem of estimating k x y in the parabolic equation u t x k x y u x y k x y u y f x y t on the basis of noisy measurements of u at discrete locations is considered subject to direct measurements of k at other discrete locations necessary conditions for optimality are derived based on a regularization formulation and the computational implementation is carried out via a finite element representation of k

universal spectral form factor for chaotic dynamics we consider the semiclassical limit of the spectral form factor k of fully chaotic dynamics starting from the gutzwiller type double sum over classical periodic orbits we set out to recover the universal behaviour predicted by random matrix theory both for dynamics with and without time reversal invariance for times smaller than half the heisenberg time th f 1 we extend the previously known expansion to include the cubic term beyond confirming the random matrix behaviour of individual spectra the virtue of that extension is that the diagrammatic rules come in sight which determine the families of orbit pairs responsible for all orders of the expansion

reduced sqp methods for parameter identification problems parameter estimation problems are formulated as constrained regularized optimization problems reduced sqp methods with bfgs update are analyzed to solve these infinite dimensional optimization problems rate of convergence results are given and numerical feasibility of the resulting algorithms is demonstrated

exp function method for constructing explicit and exact solutions of a lattice equation in this paper the exp function method is use to obtain explicit and exact solutions of a lattice equation as a result some new generalized solitonary solutions with parameters are obtained taking full advantages of the generalized solitonary solutions some known solitary wave solutions reported in open literature are derived as special cases it is shown that the exp function method with the help of symbolic computation provides a very effective and powerful new method for discrete nonlinear evolution equations in mathematical physics

action correlation of orbits through non conventional time reversal recently sieber and richter calculated semiclassically a first off diagonal contribution to the orthogonal form factor for a billiard on a surface of constant negative curvature following prior suggestions from the theory of disordered systems they considered orbit pairs with almost the same action for a generalization to systems invariant under non conventional time reversal which also belong to the orthogonal symmetry class we show here that it is necessary to redefine the configuration space by a suitable canonical transformation the distinction of this space is that it lets time reversal look conventional

finite difference lattice boltzmann model for nonlinear convection diffusion equations in this paper a finite difference lattice boltzmann lb model for nonlinear isotropic and anisotropic convection diffusion equations is proposed in this model the equilibrium distribution function is delicately designed in order to recover the convection diffusion equation exactly different from the standard lb model the temporal and spatial steps in this model are decoupled such that it is convenient to study convection diffusion problem with the non uniform grid in addition it also preserves the advantage of standard lb model that the complex valued convection diffusion equation can be solved directly the von neumann stability analysis is conducted to discuss the stability region which can be used to determine the free parameters appeared in the model to test the performance of the model a series of numerical simulations of some classical problems including the diffusion equation the nonlinear heat conduction equation the sine gordon equation the gaussian hill problem the burgersfisher equation and the nonlinear schrdinger equation have also been carried out the results show that the present model has a second order convergence rate in space and generally it is also more accurate than the standard lb model

the tanh and the sine cosine methods for compact and noncompact solutions of the nonlinear klein gordon equation the nonlinear klein gordon equation is used as a vehicle to employ the tanh method and the sine cosine method to formally derive a number of travelling wave solutions the study features a variety of solutions with distinct physical structures the work shows that one method complements the other and each method gives solutions of formal properties the obtained solutions include compactons solitons solitary patterns and periodic solutions

compactons and solitary patterns structures for variants of the kdv and the kp equations in this paper we discuss mathematical variants in higher dimensions of the kdv and the kp equations it is shown that the focusing branches of these variants exhibit compactons solitons with finite wavelength whereas the defocusing branches support solitary patterns solutions with infinite slopes or cusps the study presents a fairly complete understanding of the compact and noncompact dispersive structures

the extended tanh method for abundant solitary wave solutions of nonlinear wave equations the extended tanh method is used to establish abundant solitary wave solutions of nonlinear wave equations the obtained solutions include solitons kinks and plane periodic solutions the study is an extension to the remarkable development by malfliet 1 the extended tanh method presents a wider applicability for handling nonlinear wave equations

solitary wave solutions of nonlinear evolution and wave equations using a direct method and macsyma the direct algebraic method for constructing travelling wave solutions on nonlinear evolution and wave equations has been generalized and systematized the class of solitary wave solutions is extended to analytic rather than rational functions of the real exponential solutions of the linearized equation expanding the solutions in an infinite series in these real exponentials an exact solution of the nonlinear pde is obtained whenever the series can be summed methods for solving the nonlinear recursion relation for the coefficients of the series and for summing the series in closed form are discussed the algorithm is now suited to solving nonlinear equations by any symbolic manipulation program this direct method is illustrated by constructing exact solutions of a generalized kdv equation the kuramoto sivashinski equation and a generalized fisher equation

exact periodic solutions of the complex ginzburg landau equation three new exact periodic solutions of the complex ginzburg landau equation are obtained in terms of the weierstrass elliptic function furthermore the new periodic solutions and other shock solutions appear as their bounded limits along the real axis for particular relationships between the coefficients in the equation in the general case bounded limits are nothing but the already known pulse hole and shock solutions it is also shown that the shapes of the solutions are quite different from the shape of the usual envelope wave solution in particular the spatial structure of the new bounded periodic solutions varies in time while the pulse solution may exhibit breather like behavior

the tanh method for generalized forms of nonlinear heat conduction and burgers fisher equations generalized forms of the kdv the nonlinear heat conduction and burgers fisher equations are investigated the analysis rests mainly on the standard tanh method the focus is on the case where the parameter m is noninteger a variety of exact travelling wave solutions of distinct physical structures are formally derived

the sine cosine and the tanh methods reliable tools for analytic treatment of nonlinear dispersive equations the sine cosine method and the tanh method are used for analytic treatment of nonlinear dispersive equations nonlinear variants of boussinesq equation are used as vehicles to show the strength of these methods solutions of distinct physical structures solitons compactons solitary patterns solutions and periodic solutions are formally derived the results show that the change in physical structures of the obtained solutions depends mainly on exponents and on the coefficients of the derivatives involved

soliton solutions and doubly periodic wave solutions for a new generalized hirota satsuma coupled system in this paper a new algebraic method with symbolic computation is presented to uniformly construct a series of exact solutions for general nonlinear equations compared with most existing tanh methods the proposed method not only gives new and more general solutions but also provides a guideline to classify the various types of the solutions according to the values of some parameters for illustration we apply the proposed method to solve a new generalized hirota satsuma coupled system and explicitly construct a series of exact solutions which include the soliton solutions and elliptic doubly periodic solutions as special cases in addition the links among our proposed method the tanh method and the extended method are also clarified generally

on closed form solutions of 2 1 breaking soliton system by similarity transformations method abstract in the present research similarity transformation method via lie group theory is proposed to seek some more exact closed form solutions of the 2 1 dimensional breaking soliton system the system describes the interactions of the riemann wave along y axis and long wave along x axis some explicit solutions of breaking soliton system are attained with appropriate choices of the arbitrary functions and making use of arbitrary constants involved in the infinitesimals in order to obtain physically meaningful solutions numerical simulation is performed on the basis of graphical representation the physical analysis of solutions reveals into multi solitons periodic quadratic asymptotic and stationary profiles

spectral collocation method for the solution of the generalized burger fisher equation abstract in this paper we present a new method for solving the generalized burger fisher equation by using the collocation formula for calculating spectral differentiation matrix for chebyshev gauss lobatto point firstly theory of application of pseudospectral method on burger fisher equations is presented this method yields burger fisher equation to a system of ordinary differential equations odes secondly we use forth order runge kutta formula for the numerical integration of the system of ode the numerical results obtained by this way have been compared with the exact solution to show the efficiency of the method

dephasing representation of quantum fidelity for general pure and mixed states a general semiclassical expression for quantum fidelity loschmidt echo of arbitrary pure and mixed states is derived it expresses fidelity as an interference sum of dephasing trajectories weighed by the wigner function of the initial state and does not require that the initial state be localized in position or momentum this general dephasing representation is special in that counterintuitively all of fidelity decay is due to dephasing and none is due to the decay of classical overlaps surprising accuracy of the approximation is justified by invoking the shadowing theorem twice both for physical perturbations and for numerical errors beyond justifying the approximation the shadowing theorem makes the dephasing representation practical without shadowing it would be impossible to find numerically the precise trajectories needed in a semiclassical approximation it is shown how the general expression reduces to the previously known special forms for localized states the superiority of the general over the specialized forms is explained and supported by numerical tests for wave packets nonlocal pure states and for simple and random mixed states the tests are done in nonuniversal regimes in mixed phase space where detailed features of fidelity are important although semiclassically motivated the present approach is valid for abstract systems with a finite hilbert basis provided that the discrete wigner transform is used this makes the method applicable via a phase space approach to problems of quantum computation

the tanh coth method for solitons and kink solutions for nonlinear parabolic equations abstract the tanh coth method is used to derive solitons and kink solutions for some of the well known nonlinear parabolic partial differential equations the equations include the fisher equation newell whithead equation allen cahn equation fitzhugh nagumo equation fisher s equation and the burgers fisher equation the new tanh coth approach provides abundant solitons and kink solutions in addition to the existing ones the power of this manageable method is confirmed

action correlations and random matrix theory the correlations in the spectra of quantum systems are intimately related to correlations which are of genuine classical origin and which appear in the spectra of actions of the classical periodic orbits of the corresponding classical systems we review this duality and the semiclassical theory which brings it about the conjecture that the quantum spectral statistics are described in terms of random matrix theory leads to the proposition that the classical two point correlation function is also given in terms of a universal function we study in detail the spectrum of actions of the baker map and use it to illustrate the steps needed to reveal the classical correlations their origin and their relation to symbolic dynamics

general solutions with solitary patterns for the defocusing branch of the nonlinear dispersive k n n equations in higher dimensional spaces in this work the defocusing branch of the genuinely nonlinear dispersive k n n equation that exhibits solutions with solitary patterns is investigated the equation with constant coefficients to the derivatives is examined in one two and three dimensional spaces general formulas for solutions with solitary patterns are developed for all positive integers n n 1 two sets of entirely new formulas one set produces solutions for even integers n whereas the second set produces solutions in opposite directions for odd integers n n 1 are established

a generalized f expansion method with symbolic computation exactly solving broer kaup equations abstract in this paper a generalized f expansion method is applied to construct exact solutions of the 2 1 dimensional broer kaup equations as a result many general exact non travelling wave and coefficient function solutions are obtained including single and combined non degenerate jacobi elliptic function solutions soliton like solutions and trigonometric function solutions each of which contains two arbitrary functions compared with most existing f expansion methods the proposed method gives new and more general exact solutions more importantly with the aid of symbolic computation the method provides a powerful mathematical tool to solve a large many nonlinear partial differential equations

application of the g g expansion method to kawahara type equations using symbolic computation abstract in this paper kawahara type equations are selected to illustrate the effectiveness and simplicity of the g g expansion method with the aid of a symbolic computation system three types of more general traveling wave solutions including hyperbolic functions trigonometric functions and rational functions with free parameters are constructed solutions concerning solitary and periodic waves are also given by setting the two arbitrary parameters involved in the traveling waves as special values

a unified rational expansion method to construct a series of explicit exact solutions to nonlinear evolution equations a unified basic frame of rational expansion methods is presented which leads to closed form solutions of nonlinear evolution equations nlees the new unified algorithms are given to find exact rational formal polynomial solutions of nlees in terms of jacobi elliptic functions solutions of the riccati equation and solutions of the generalized riccati equation they can be implemented in symbolic computation system maple as applications of the methods we choose some physical significance nlees to illustrate the methods as a consequence we not only can successfully obtain the solutions found by most existing jacobi elliptic function methods and tanh methods but also find other new and more general solutions at the same time

quasi newton methods and unconstrained optimal control problems we prove a mesh independence result for the bfgs method in hilbert space and apply it to a class of unconstrained optimal control problems a new fourth order discretization scheme is used in the i

a generalized auxiliary equation method and its application to 2 1 dimensional korteweg de vries equations a generalized auxiliary equation method is proposed for constructing more general exact solutions of nonlinear partial differential equations with the aid of symbolic computation we choose the 2 1 dimensional korteweg de vries equations to illustrate the validity and advantages of this method as a result many new and more general exact non travelling wave and coefficient function solutions are obtained which include soliton like solutions triangular like solutions single and combined non degenerate jacobi elliptic wave function like solutions and weierstrass elliptic doubly like periodic solutions

the local convergence of broyden like methods on lipschitzian problems in hilbert spaces the classical local convergence analysis for broyden s method requires a finite number of real variables holder continuity of the jacobian and a rather accurate initial approximation b 0 here these three conditions are relaxed to allow for lipschitz continuous hilbert space operators that can be reasonably well approximated by a linear operator b that is close to b 0 up to an arbitrary compact perturbation to achieve local and r linear convergence broyden s method is modified by a very mild line search condition in case of a continuously differentiable system in euclidean space we obtain r superlinear convergence without restricting b 0 or requiring the jacobian to be holder continuous

form factor for a family of quantum graphs an expansion to third order for certain types of quantum graphs we show that the random matrix form factor can be recovered to at least third order in the scaled time from periodic orbit theory we consider the contributions from pairs of periodic orbits represented by diagrams with up to two self intersections connected by up to four arcs and explain why all other diagrams are expected to give higher order corrections only for a large family of graphs with ergodic classical dynamics the diagrams that exist in the absence of time reversal symmetry sum to zero the mechanism for this cancellation is rather general which suggests that it also applies at higher orders in the expansion this expectation is in full agreement with the fact that in this case the linear contribution the diagonal approximation already reproduces the random matrix form factor for 1 for systems with time reversal symmetry there are more diagrams which contribute at third order we sum these contributions for quantum graphs with uniformly hyperbolic dynamics obtaining 2 3 in agreement with random matrix theory as in the previous calculation of the leading order correction to the diagonal approximation we find that the third order contribution can be attributed to exceptional orbits representing the intersection of diagram classes

general compactons solutions for the focusing branch of the nonlinear dispersive k n n equations in higher dimensional spaces in this paper we will study the focusing branch of the genuinely nonlinear dispersive k n n equation that exhibits compactons solitons with finite wavelengths the equation will be studied in one two and three dimensional spaces general formulas for compactons solutions are developed for all positive integers n n 1 two sets of entirely new formulas one set produces compactons for even integers n whereas the second set produces compactons and anticompactons for odd integers n n 1 are established

variants of the generalized kdv equation with compact and noncompact structures abstract in this paper nonlinear dispersive variants of the generalized kdv equation are investigated the compact and the noncompact physical structures are studied two general formulas for the focusing branch and the defocusing branch that are of substantial interest are formally derived

exp function method for riccati equation and new exact solutions with two arbitrary functions of 2 1 dimensional konopelchenko dubrovsky equations in this paper new exact solutions with two arbitrary functions of the 2 1 dimensional konopelchenko dubrovsky equations are obtained by means of the riccati equation and its generalized solitary wave solutions constructed by the exp function method it is shown that the exp function method provides us with a straightforward and important mathematical tool for solving nonlinear evolution equations in mathematical physics

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

the compound g g expansion method and double non traveling wave solutions of 2 1 dimensional nonlinear partial differential equations abstract to seek the exact double non traveling wave solutions of nonlinear partial differential equations the compound g g expansion method is firstly proposed in this paper with the aid of symbolic computation this new method is applied to construct double non traveling wave solutions of 2 1 dimensional painleve integrable burgers equation and 2 1 dimensional breaking soliton equation as a result abundant double non traveling wave solutions including double hyperbolic function solutions double trigonometric function solutions double rational solutions and a series of complexiton solutions of these two equations are obtained via the proposed method these exact solutions contain arbitrary functions which may be helpful to explain some complex phenomena when the parameters are taken as special values the double solitary like wave solutions can be derived from double hyperbolic function solutions furthermore the time evolutions of double solitary like wave solutions are discussed in detail

weierstrass semi rational expansion method and new doubly periodic solutions of the generalized hirota satsuma coupled kdv system in the paper with the aid of symbolic computation we investigate the generalized hirota satsuma coupled kdv system via our weierstrass semi rational expansion method presented recently using the rational expansion of weierstrass elliptic function and its first order derivative as a consequence three families of new weierstrass elliptic function solutions via weierstrass elliptic function p g2 g3 and its first order derivative p g2 g3 moreover the corresponding new jacobi elliptic function solutions and solitary wave solutions are also presented and when these solitary wave solutions approach to some constants

the extended tanh method and its applications for solving nonlinear physical models the extended tanh method with a computerized symbolic computation is used for constructing the travelling wave solutions of coupled nonlinear equations arising in physics the obtained solutions include solitons kinks and plane periodic solutions the applied method will be used in further works to establish more entirely new solutions for other kinds of nonlinear evolution equations arising in physics

numerical solutions of coupled burgers equations with time and space fractional derivatives in this paper by introducing the fractional derivative in the sense of caputo the adomian decomposition method is directly extended to study the coupled burgers equations with time and space fractional derivatives as a result the realistic numerical solutions are obtained in a form of rapidly convergent series with easily computable components the figures show the effectiveness and good accuracy of the proposed method

a generalized new auxiliary equation method and its application to the 2 1 dimensional breaking soliton equations abstract in this paper the new auxiliary equation method sirendaoreji a new auxiliary equation and exact travelling wave solutions of non linear equations phys lett a 356 2006 124 130 is improved and a generalized new auxiliary equation method is proposed to construct more general exact solutions of non linear partial differential equations with the aid of symbolic computation we choose the 2 1 dimensional breaking soliton equations to illustrate the validity and advantages of the method as a result many new and more general non travelling wave and coefficient function solutions are obtained including soliton like solutions trigonometric function solutions exponential solutions

a construction of compact and noncompact solutions for nonlinear dispersive equations of even order a construction of compact and noncompact solutions for nonlinear dispersive partial differential equations of even order is considered two model equations of even orders k 4 are adopted to carry out this study the analysis reveals the presence of distinct roots of different indices that play a significant role in the solutions

state and parameter estimation in 1 d hyperbolic pdes based on an adjoint method an optimal estimation method for state and distributed parameters in 1 d hyperbolic system based on adjoint method is proposed in this paper a general form of the partial differential equations governing the dynamics of system is first introduced in this equation the initial condition or state variable as well as some empirical parameters are supposed to be unknown and need to be estimated the lagrangian multiplier method is used to connect the dynamics of the system and the cost function defined as the least square error between the simulation values and the measurements the adjoint state method is applied to the objective functional in order to get the adjoint system and the gradients with respect to parameters and initial state the objective functional is minimized by broyden fletcher goldfarb shanno bfgs method due to the non linearity of both direct and adjoint system the nonlinear explicit lax wendroff scheme is used to solve them numerically the presented optimal estimation approach is validated by two illustrative examples the first one about state and parameter estimation in a traffic flow and the second one in an overland flow system

estimation of two phase petroleum reservoir properties by regularization abstract an algorithm is developed based on the theory of regularization and on spline approximation to estimate the absolute permeability in two phase petroleum reservoirs from noisy well pressure data the regularization feature of the algorithm converts the ill posed estimation problem to a well posed one the algorithm which employs the partial conjugate gradient method of nazareth as its core minimization technique automatically chooses the regularization parameter based on the non regularized estimation it is shown that regularized estimation is more stable and insensitive to the choice of initial guess as compared to non regularized conventional estimation

on two approaches of finding exact solutions to nonlinear evolution equations in this work we give some discussions on the sec q tanh q method of finding exact solutions to the nonlinear evolution equations presented by liu and jiang we conclude that the method is just one special case of the generalized projective riccati equation method therefore these deformed hyperbolic function solutions do not pertain to a new class then based on the generalized projective riccati equation method more exact solutions of the hirota satsuma coupled kdv systems are obtained

a new rational auxiliary equation method and exact solutions of a generalized zakharov system a new rational auxiliary equation method for obtaining exact traveling wave solutions of constant coefficient nonlinear partial differential equations of evolution is proposed its effectiveness is evinced by obtaining exact solutions of a generalized zakharov system some of which are new it is shown that the g g and the generalized projective ricatti expansion methods are special cases of the auxiliary equation method further due the solutions obtained four other new and practicable rational methods are deduced

the tanh method for traveling wave solutions of nonlinear equations in this work we employ the tanh method for traveling wave solutions of nonlinear equations the study is extended to equations that do not have tanh polynomial solutions the efficiency of the method is demonstrated by applying it for a variety of selected equations

semiclassical form factor for spectral and matrix element fluctuations of multidimensional chaotic systems we present a semiclassical calculation of the generalized form factor kab tau which characterizes the fluctuations of matrix elements of the operators a and b in the eigenbasis of the hamiltonian of a chaotic system our approach is based on some recently developed techniques for the spectral form factor of systems with hyperbolic and ergodic underlying classical dynamics and f 2 degrees of freedom that allow us to go beyond the diagonal approximation first we extend these techniques to systems with f 2 then we use these results to calculate kab tau we show that the dependence on the rescaled time tau time in units of the heisenberg time is universal for both the spectral and the generalized form factor furthermore we derive a relation between kab tau and the classical time correlation function of the weyl symbols of a and b