generalized dirichlet to neumann map for moving initial boundary value problems we present an algorithm for characterizing the generalized dirichlet to neumann map for moving initial boundary value problems this algorithm is derived by combining the so called global relation which couples the initial and boundary values of the problem with a new method for inverting certain one dimensional integrals this new method is based on the spectral analysis of an associated ordinary differantial equation and on the use of the d bar formalism as an illustration the neumann boundary value for the linearized schrodinger equation is determined in terms of the dirichlet boundary value and of the initial condition

nonlinear self adjointness of a 2d generalized second order evolution equation abstract we study the nonlinear self adjointness of a general class of quasilinear 2d second order evolution equations which do not possess variational structure for this purpose we use the method of ibragimov devised and developed recently this approach enables one to establish the conservation laws for any differential equation we first obtain conditions determining the self adjoint sub class in the general case then we establish the conservation laws for important particular cases the ricci flow equation the modified ricci flow equation and the nonlinear heat equation

renormalisation theory of the self avoiding levy flight the self avoiding levy flight salf in d dimensions with levy exponent mu is formulated as a geometrical equilibrium statistical mechanical problem a direct renormalisation theory based on modern field theoretic techniques is used to derive the critical exponents and the end to end distance probability function through first order in epsilon 2 mu d the non perturbative structure of the probability function is characterised by a universal scaling function the salf represents a simple many body system that can assume a continuum of values of epsilon near zero

reciprocal transformations of two component hyperbolic systems and their invariants abstract criteria for the equivalence under reciprocal transformations of two component hyperbolic systems are established in terms of reciprocal invariants these results are applied to a 1 1 dimensional isentropic gasdynamics system to determine reciprocal equivalence to the canonical system with a polytropic gas law the four parameter model pressure density relations for which this reciprocal equivalence holds are parameterized in terms of the lagrangian signal speed

existence of an exact solution for a one phase stefan problem with nonlinear thermal coefficients from tirskii s method abstract the mathematical analysis of a one phase lame clapeyron stefan problem with nonlinear thermal coefficients following g a tirskii two exact solutions of stefan s nonlinear problem sov phys dokl 4 1959 288 292 is obtained two related cases are considered one of them has a temperature condition on the fixed face x 0 and the other one has a flux condition of the type q 0 t q 0 0 we obtain in both cases sufficient conditions for data in order to have the existence of an explicit solution of a similarity type which is given by using a double fixed point

invariant conservation law preserving discretizations of linear and nonlinear wave equations symmetry and conservation law preserving finite difference discretizations are obtained for linear and nonlinear one dimensional wave equations on five and nine point stencils using the theory of lie point symmetries of difference equations and the discrete direct multiplier method of conservation law construction in particular for the linear wave equation an explicit five point scheme is presented that preserves the discrete analogs of its basic geometric point symmetries and six of the corresponding conservation laws for a class of nonlinear wave equations arising in hyperelasticity a nine point implicit scheme is constructed preserving four point symmetries and three local conservation laws other discretizations of the nonlinear wave equations preserving different subsets of conservation laws are discussed

second noether theorem for quasi noether systems quasi noether differential systems are more general than variational systems and are quite common in mathematical physics they include practically all differential systems of interest at least those that have conservation laws in this paper we discuss quasi noether systems that possess infinite dimensional infinite symmetries involving arbitrary functions of independent variables for quasi noether systems admitting infinite symmetries with arbitrary functions of all independent variables we state and prove an extension of the second noether theorem in addition we prove that infinite sets of conservation laws involving arbitrary functions of all independent variables are trivial and that the associated differential system is under determined we discuss infinite symmetries and infinite conservation laws of two important examples of non variational quasi noether systems the incompressible euler equations and the navier stokes equations in vorticity formulation and we show that the infinite sets of conservation laws involving arbitrary functions of all independent variables are trivial we also analyze infinite symmetries involving arbitrary functions of not all independent variables prove that the fluxes of conservation laws in these cases are total divergences on solutions and demonstrate examples of this situation

a complete renormalization group trajectory between two fixed points we give a rigorous nonperturbative construction of a massless discrete trajectory for wilson s exact renormalization group the model is a three dimensional euclidean field theory with a modified free propagator the trajectory realizes the mean field to critical crossover from the ultraviolet gaussian fixed point to an analog recently constructed by brydges mitter and scoppola of the wilson fisher nontrivial fixed point

a new approach to the numerical solution of weakly singular volterra integral equations we consider linear weakly singular volterra integral equations of the second kind with kernels of the form k x v x v k x v 0 1 or k x v log x v k x v k x v being a smooth function the solutions of such equations may exhibit a singular behaviour in the neighbourhood of the initial point of the interval of integration by a transformation of the unknown function we obtain an equation which is still weakly singular but whose solution is as smooth as we like this resulting equation is then solved by standard product integration methods

explicit solution for a stefan problem with variable latent heat and constant heat flux boundary conditions abstract in voller swenson and paola v r voller j b swenson c paola an analytical solution for a stefan problem with variable latent heat int j heat mass transfer 47 2004 5387 5390 and lorenzo trueba and voller j lorenzo trueba v r voller analytical and numerical solution of a generalized stefan problem exhibiting two moving boundaries with application to ocean delta formation j math anal appl 366 2010 538 549 a model associated with the formation of sedimentary ocean deltas is studied through a one phase stefan like problem with variable latent heat motivated by these works we consider a two phase stefan problem with variable latent of fusion and initial temperature and constant heat flux boundary conditions we obtain the sufficient condition on the data in order to have an explicit solution of a similarity type of the corresponding free boundary problem for a semi infinite material moreover the explicit solution given in the first quoted paper can be recovered for a particular case by taking a null heat flux condition at the infinity

the adjoint equation method for constructing first integrals of difference equations a new method for finding first integrals of discrete equations is presented it can be used for discrete equations which do not possess a variational lagrangian or hamiltonian formulation the method is based on a newly established identity which links symmetries of the underlying discrete equations solutions of the discrete adjoint equations and first integrals the method is applied to an invariant mapping and to discretizations of second order and third order ordinary differential equations in examples the set of independent first integrals makes it possible to find the general solution of the discrete equations

application of reciprocal backlund transformations to a class of nonlinear boundary value problems it is shown that reciprocal backlund transformations may be used to reduce an important class of nonlinear boundary value problems for higher order nonlinear diffusion equations to linear canonical boundary value problems

reciprocal transformations in 2 1 dimensions reciprocal backlund transformations are introduced for nonlinear integro differential equations in 2 1 dimensions invariance under such transformations is investigated

constrained walks and self avoiding walks implications for protein structure determination we prove that n step walks and self avoiding walks on the 2d honeycomb 2d square 3d diamond and 3d cubic lattices can be uniquely characterized canonized with no more than n euclidian distances we also demonstrate that these canonical distances can be obtained with o n physical measurements finally while the protein folding problem on lattices is known to be strongly np hard we prove that lattice protein structures of size n matching o n canonical distance measurements can be determined in linear time

lie symmetry analysis and conservation law of variable coefficient davey stewartson equation abstract a variable coefficient davey stewartson vcds equation is investigated in this paper infinitesimal generators and symmetry groups are presented by the lie group method and the optimal system is presented with adjoint representation based on the optimal system similarity reductions to partial differential equations pdes are obtained then some pdes are reduced to ordinary differential equations odes by two dimensional subalgebras and the similarity solutions are provided including periodic solutions and elliptic function solutions with lagrangian it is shown that vcds is nonlinearly self adjoint furthermore based on nonlinear self adjointness conservation laws for vcds equation are derived

time fractional 2 1 dimensional wu zhang system dispersion analysis similarity reductions conservation laws and exact solutions abstract this paper examines the time fractional 2 1 dimensional wu zhang system describing dispersive long waves the dispersion relation of waves has been obtained from linear analysis and used to find the phase and group velocity the dispersion relation shows an anomalous dispersion of waves lie symmetries and the corresponding similarity reductions are carried out using riemann liouville fractional derivative and the order of the system is reduced to lower dimension furthermore the system is analysed for nonlinear self adjointness and the conservation laws are obtained associated with infinitesimal symmetries by applying new conservation theorem the adjoint variables are used to convert conservation laws into original dependent variables the exponential rational function method is employed to find exact solutions revealing kink and bell type profiles the effect of fractional order on the wave profile of solutions is discussed graphically

loop soliton interaction in an integrable nonlinear telegraphy model reciprocal and backlund transformations an integrable telegraphy equation linked in turn to the geometry of pseudospherical surfaces and a class of model nonlinear elastic stress strain laws descriptive of ideally hard material response is investigated a constant coefficient ideal formalism is introduced which leads to a reciprocal transformation between this nonlinear telegraphy equation and a system compatible with the classical sine gordon equation a backlund transformation is then constructed which is used to analyse two loop soliton interaction the latter exhibits a novel exchange particle phenomenon

inverse transformations and the reduction of nonlinear dirichlet problems involutory transformations are introduced which allow the solution of a class on nonlinear dirichlet problems the application of coupled involutory and backlund transformations is also described

analysis of lie symmetries with conservation laws and solutions for the generalized 3 1 dimensional time fractional camassa holm kadomtsev petviashvili equation abstract in this paper under investigated is a generalized 3 1 dimensional camassa holm kadomtsev petviashvili gch kp equation which describes the role of dispersion in the formation of patterns in liquid drops with the help of the semi inverse method the euler lagrange equation and agrawal s method the time fractional gch kp equation is derived in the sense of riemann liouville fractional derivatives further the symmetry of the 3 1 dimensional time fractional gch kp equation is studied by fractional order symmetry meanwhile based on the new conservation theorem the conservation laws of 3 1 dimensional time fractional gch kp equation are constructed finally the solutions to the equation are given via a bilinear method and the radial basis functions rbfs meshless approach

topological entropy on saddle sets in p2 we consider hyperbolic sets of saddle type for holomorphic mappings in p our main result relates topological entropy on such sets to a normal families condition on local unstable manifolds

on the nonlinear self adjointness of a class of fourth order evolution equations in this paper we study the property of nonlinear self adjointness for a class of nonlinear fourth order equation it is shown that if an equation itself is a conservation law then it possesses the property of nonlinear self adjointness and hence it can be rewritten in an equivalent strictly self adjoint form the property of nonlinear self adjointness is used to obtain all nontrivial conservation laws for the class under consideration

on a two phase free boundary problem a two phase free boundary problem associated with the burgers equation is considered the problem is reduced to a system of nonlinear integral equations which is analysed and shown to have a unique solution the system admits a two component shock solution which travels with the same velocity as that of the free boundary the stability analysis of such a solution shows the existence of stability and instability regions according to different values of the parameters characterizing the system

explicit solutions for a two phase unidimensional lame clapeyron stefan problem with source terms in both phases a two phase stefan problem with heat source terms of a general similarity type in both liquid and solid phases for a semi infinite phase change material is studied we assume the initial temperature is a negative constant and we consider two different boundary conditions at the fixed face x 0 a constant temperature or a heat flux of the form q0 t q0 0 the internal heat source functions are given by gj x t lt j x2ajt j 1 solid phase j 2 liquid phase where j j are functions with appropriate regularity properties is the mass density l is the fusion latent heat by unit of mass aj2 is the diffusion coefficient x is the spatial variable and t is the temporal variable we obtain for both problems explicit solutions with a restriction for data only for the second boundary conditions on x 0 moreover the equivalence of the two free boundary problems is also proved we generalize the solution obtained in j l menaldi d a tarzia generalized lame clapeyron solution for a one phase source stefan problem comput appl math 12 2 1993 123 142 for the one phase stefan problem finally a particular case where j j 1 2 are of exponential type given by j x exp x dj 2 with x and dj r is also studied in details for both boundary temperature conditions at x 0 this type of heat source terms is important through the use of microwave energy following e p scott an analytical solution and sensitivity study of sublimation dehydration within a porous medium with volumetric heating j heat transfer 116 1994 686 693 we obtain a unique solution of the similarity type for any data when a temperature boundary condition at the fixed face x 0 is considered a similar result is obtained for a heat flux condition imposed on x 0 if an inequality for parameter q0 is satisfied

a family of wave equations with some remarkable properties we consider a family of homogeneous nonlinear dispersive equations with two arbitrary parameters conservation laws are established from the point symmetries and imply that the whole family admits square integrable solutions recursion operators are found for two members of the family investigated for one of them a lax pair is also obtained proving its complete integrability from the lax pair we construct a miura type transformation relating the original equation to the korteweg de vries kdv equation this transformation on the other hand enables us to obtain solutions of the equation from the kernel of a schrodinger operator with potential parametrized by the solutions of the kdv equation in particular this allows us to exhibit a kink solution to the completely integrable equation from the 1 soliton solution of the kdv equation finally peakon type solutions are also found for a certain choice of the parameters although for this particular case the equation is reduced to a homogeneous second order nonlinear evolution equation

classical and potential symmetries for a generalized fisher equation in this work we consider a generalized fisher equation and we have considered this equation from the point of view of the theory of symmetry reductions in partial differential equations generalizations of the fisher equation are needed to more accurately model complex diffusion and reaction effects found in many biological systems the reductions to ordinary differential equations are derived from the optimal system of subalgebras and new exact solutions are obtained the potential system has been achieved from the complete list of the conservation laws potential symmetries which are not local symmetries are carried out for the generalized fisher equation these symmetries lead to the linearization of the equation by non invertible mappings

a cauchy problem in nonlinear heat conduction a cauchy problem on the semiline for a nonlinear diffusion equation is considered with a boundary condition corresponding to a prescribed thermal conductivity at the origin the problem is mapped into a moving boundary problem for the linear heat equation with a robin type boundary condition such a problem is then reduced to a linear integral volterra equation of ii type which admits a unique solution

group classification and conservation laws for a two dimensional generalized kuramoto sivashinsky equation abstract the two dimensional anisotropic kuramoto sivashinsky equation is a fourth order nonlinear evolution equation in two spatial dimensions that arises in sputter erosion and epitaxial growth on vicinal surfaces a generalization of this equation is proposed and studied via group analysis methods the complete group classification of this generalized kuramoto sivashinsky equation is carried out it is classified according to the property of the self adjointness and the corresponding conservation laws are established

symmetry conserved quantities and moments in diffusive equations abstract in this note we show that there is an intimate connection between the symmetries of a partial differential equation and the time behavior of its moments we also derive closed form expressions for certain conserved quantities and polynomial solutions we discuss the heat and fokker planck equations

nonlinear self adjointness of a generalized fifth order kdv equation the new concepts of self adjoint equations formulated by ibragimov and gandarias are applied to a class of fifth order evolution equations then from ibragimov s theorem on conservation laws conservation laws for the generalized kawahara equation simplified kahawara equation and modified simplified kawahara equation are established

integrating factors adjoint equations and lagrangians integrating factors and adjoint equations are determined for linear and non linear differential equations of an arbitrary order the new concept of an adjoint equation is used for construction of a lagrangian for an arbitrary differential equation and for any system of differential equations where the number of equations is equal to the number of dependent variables the method is illustrated by considering several equations traditionally regarded as equations without lagrangians noether s theorem is applied to the maxwell equations

the probability of the quantum diffusion controlled reaction of a species pair abstract the kinetics of diffusion controlled bimolecular reaction a b p products is investigated in the case when the motion of the diffusing particle is governed by the quantum markovian master equation for a density matrix in the site representation in the framework of the discrete model of random walks definitions are given of the survival and reaction probabilities for a pair of particle species a and b and of the rate constant a method for calculating these quantities is proposed formulae are obtained for the survival and reaction probabilities and the rate constant corresponding to chemical interaction between the particles only when they are at one and the same site

application of linked backlund transformations to nonlinear boundary value problems a class of nonlinear boundary value problems is reduced to linear canonical form by a combination of backlund transformations

time fractional generalized boussinesq equation for rossby solitary waves with dissipation effect in stratified fluid and conservation laws as well as exact solutions abstract construct fractional order model to describe rossby solitary waves can provide more pronounced effects and deeper insight for comprehending generalization and evolution of rossby solitary waves in stratified fluid in the paper from the quasi geostrophic vorticity equation with dissipation effect and complete coriolis force based on the multi scale analysis and perturbation method a classical generalized boussinesq equation is derived to describe the rossby solitary waves in stratified fluid further by employing the reduction perturbation method the semi inverse method the agrawal method we derive the euler lagrangian equation of classical generalized boussinesq equation and obtain the time fractional generalized boussinesq equation without dissipation effect by using lie group analysis method the conservation laws of time fractional boussinesq equation are given finally with the help of the improved g g expansion method the exact solutions of the above equation are generated meanwhile in order to consider the dissipation effect we have to derive the approximate solutions by adopting the new iterative method we remark that the fractional order model can open up a new window for better understanding the waves in fluid

a numerical scheme for solving special class of nonlinear diffusion convection equation the nonlinear diffusion convection equations arising from the theory of transport in porous media is analyzed the problem under analysis has the email protected email protected email protected email protected zd c email protected z k c where d c d 0c m 1 vc m 2 and k c k 0c m 2 1 vc m 1 the behavior of solutions when m 1 and 00 numerical and analytical results compared for the cases m 0 1 and numerical results for m 2 and m 0 5 are stated

comment on the paper on conservation laws by lie symmetry analysis for 2 1 dimensional bogoyavlensky konopelchenko equation in wave propagation by s saha ray abstract in a recent paper referred to in the title the author used the concept of quasi self adjointness to obtain conservation laws for a system of the 2 1 dimensional bogoyavlensky konopelchenko equation apart from the adjoint system of equations all the results on the quasi self adjointness and the subsequent conservation laws obtained are inaccurate in this comment we clarify these inaccuracies and also generate conservation laws for a potential form of the underlying equation through noether theorem

a new conservation theorem a general theorem on conservation laws for arbitrary differential equations is proved the theorem is valid also for any system of differential equations where the number of equations is equal to the number of dependent variables the new theorem does not require existence of a lagrangian and is based on a concept of an adjoint equation for non linear equations suggested recently by the author it is proved that the adjoint equation inherits all symmetries of the original equation accordingly one can associate a conservation law with any group of lie lie backlund or non local symmetries and find conservation laws for differential equations without classical lagrangians

quantum markovian master equation theory of particle migration in a stochastic medium abstract the problem of quasi particle motion in a stochastic medium is investigated under the supposition that it is a markovian process the phenomenological approach to this problem starts from the well known quantum markovian master equation the paper is devoted to the construction of the so called dissipative terms of the master equation a special form of dissipative terms is suggested the quasi particle performing random walks from site to site in a crystal lattice and the diffusing particle in a stochastic continuum are discussed as particular cases of an open quantum system an evolution of which may be described by means of a markovian master equation containing the dissipative terms constructed with the help of the suggested method

nonlinear self adjointness a criterion for linearization of pdes in this communication we show that the property of nonlinear self adjointness is conserved by an invertible point transformation we use this property to give necessary conditions for the existence of an invertible point transformation mapping of a given partial differential equation pde to a linear pde

statistical theory of systems of created reactive species abstract a statistical theory is developed for systems in which the creation of identical species a in a condensed medium is accompanied by their decay as a result of the reaction a a p products many species distribution functions which describe the processes of creation and decay of species are defined on the basis of statistical ensembles equations for these functions are obtained the theory is a statistical validation of the author s earlier kinetic theories of reactive species accumulation and bimolecular reactions in condensed media

comments on the paper conservation laws of the 2 1 dimensional kp equation and burgers equation with variable coefficients and cross terms by li hua zhang the recent paper mentioned in the title contains a confusing statement on computing conservation laws corresponding to symmetries of nonlinearly self adjoint differential equations the present brief article contains clarifying comments

explicit solutions to the two phase stefan problem for storm type materials a reciprocal transformation is employed to reduce a two phase stefan problem in nonlinear heat conduction into a form which admits a class of exact solutions analogous to the classical neumann solution the problem is considered for materials of storm type rogers 1985 j phys a math gen 18 105 9 two related cases are considered one of them has a flux condition of the type q 0 t 1 2 q 0 0 and the existence and uniqueness of the solution is proved when q 0 satisfies a certain inequality which generalizes the work of tarzia 1981 q appl math 39 491 7 obtained for constant thermal coefficients the other one has a temperature condition on the fixed face and the existence and uniqueness is proved for all data

traveling wave solutions and conservation laws for nonlinear evolution equation in this work the riccati bernoulli sub ordinary differential equation and modified tanh coth methods are used to reach soliton solutions of the nonlinear evolution equation we acquire new types of traveling wave solutions for the governing equation we show that the equation is nonlinear self adjoint by obtaining suitable substitution therefore we construct conservation laws for the equation using new conservation theorem the obtained solutions in this work may be used to explain and understand the physical nature of the wave spreads in the most dispersive medium the constraint condition for the existence of solitons is stated some three dimensional figures for some of the acquired results are illustrated

on renormalisation of fluctuations at the onset of a centre manifold the author considers a dissipative reactive system driven far from thermodynamic equilibrium and sustaining a locally attractive centre manifold beyond a symmetry breaking instability the author derives a functional equation for the renormalised diffusion pressure this coefficient gives autocorrelations for intrinsic fluctuations and depends on the bifurcation parameter the system is subject to the following realistic restrictions i the temporal organisation lying beyond the instability can be accounted for by the existence of a centre manifold ii the effective equilibrium energy averaged with respect to the stationary distribution about the centre manifold is independent of the bifurcation parameter

application of a reciprocal transformation to a two phase stefan problem a reciprocal transformation is employed to reduce a two phase stefan problem in nonlinear heat conduction to a form which admits a class of exact solutions analogous to the classical newmann solution

reciprocal auto backlund transformations invariant backlund transformations of reciprocal type are derived for a class of n 1 th order conservation laws a new auto backlund transformation for the harry dym equation is presented as a special case of the analysis

a two phase free boundary problem for a nonlinear diffusion convection equation a two phase free boundary problem associated with a diffusion convection equation is considered the problem is reduced to a system of nonlinear integral equations which admits a unique solution for small times the system admits an explicit two component solution corresponding to a two component shock wave of the burgers equation the stability of such a solution is also discussed

immiscible two phase flow in a porous medium utilization of a laplace transform boost a boost operator is defined for the laplace transform it is used in conjunction with the laplace transform to solve the diffusion equation on a domain with multiple moving boundaries this problem arises in the study of immiscible multiphase flow in a finite medium including end effects extensions of this method to the solution of other linear differential equations are conceivable

on the exactly solvable equation s_t beta s gamma 2 s_x _x alpha beta s gamma 2 s_x occurring in two phase flow in porous media the symmetry approach of fokas j math phys 21 1980 pp 1318 1325 is used to show that the most general equation of the form s t g s s xx f s s x dg ds ne 0 which is exactly solvable is equivalent to the equation s t beta s gamma 2 s x x alpha beta s gamma 2 s x this equation is then mapped to the linear heat equation through a series of backlund transformations the above result is used to solve an initial boundary value problem modeling the process of waterflooding i e the displacement of oil initially in a porous reservoir by continuously injected water

localized partial traps in diffusion processes and random walks reaction diffusion equations in which the reaction is described by a sink term consisting of a sum of delta functions are studied it is shown that the laplace transform of the reactive green s function can be analytically expressed in terms of the green s function for diffusion in the absence of reaction moreover a simple relation between the green s functions satisfying the radiation boundary condition and the reflecting boundary condition is obtained several applications are presented and the formalism is used to establish the relationship between the time dependent geminate recombination yield and the bimolecular reaction rate for diffusion influenced reactions finally an analogous development for lattice random walks is presented

the dirichlet to neumann map for a nonlinear diffusion convection equation a method for constructing the dirichlet to neumann map for a nonlinear diffusion convection equation is presented the problem is reduced to the solution of a nonlinear integral equation in one independent variable existence and uniqueness of the solution may be proven for small times via a contraction mapping technique

nonlinear self adjointness and conservation laws the general concept of nonlinear self adjointness of differential equations is introduced it includes the linear self adjointness as a particular case moreover it embraces the strict self adjointness definition 1 and quasi self adjointness introduced earlier by the author it is shown that the equations possessing nonlinear self adjointness can be written equivalently in a strictly self adjoint form by using appropriate multipliers all linear equations possess the property of nonlinear self adjointness and hence can be rewritten in a nonlinear strictly self adjoint form for example the heat equation ut u 0 becomes strictly self adjoint after multiplying by u 1 conservation laws associated with symmetries are given in an explicit form for all nonlinearly self adjoint partial differential equations and systems

product integration methods for second kind abel integral equations the construction and convergence of high order product integration methods for the second kind abel equation are discussed and the results of de hoog and weiss are generalised backward difference methods are introduced and numerical results are presented which verify the theoretical rates of convergence