相关论文: Computation of conservation laws for nonlinear lat…
A new algorithm for the symbolic computation of polynomial conserved densities for systems of nonlinear evolution equations is presented. The algorithm is implemented in Mathematica. The program condens.m automatically carries out the…
A new method for the computation of conserved densities of nonlinear differential-difference equations is applied to Toda lattices and discretizations of the Korteweg-de Vries and nonlinear Schrodinger equations. The algorithm, which can be…
A direct method for the computation of polynomial conservation laws of polynomial systems of nonlinear partial differential equations (PDEs) in multi-dimensions is presented. The method avoids advanced differential-geometric tools. Instead,…
Three symbolic algorithms for testing the integrability of polynomial systems of partial differential and differential-difference equations are presented. The first algorithm is the well-known Painlev\'e test, which is applicable to…
A method for symbolically computing conservation laws of nonlinear partial differential equations (PDEs) in multiple space dimensions is presented in the language of variational calculus and linear algebra. The steps of the method are…
Algorithms for the symbolic computation of polynomial conservation laws, generalized symmetries, and recursion operators for systems of nonlinear differential-difference equations (DDEs) are presented. The algorithms can be used to test the…
New extra series of conserved densities for the polytropic gas model and nonlinear elasticity equation are obtained without any references to the recursion operator or to the Lax operator formalism. Our method based on the utilization of…
An algorithmic method using conservation law multipliers is introduced that yields necessary and sufficient conditions to find invertible mappings of a given nonlinear PDE to some linear PDE and to construct such a mapping when it exists.…
A method based on infinite parameter conservation laws is described to factor linear differential operators out of nonlinear partial differential equations (PDEs) or out of differential consequences of nonlinear PDEs. This includes a…
Conservation laws are computed for various nonlinear partial differential equations that arise in elasticity and acoustics. Using a scaling homogeneity approach, conservation laws are established for two models describing shear wave…
The conservation laws for a class of nonlinear equations with variable coefficients on discrete and noncommutative spaces are derived. For discrete models the conserved charges are constructed explicitly. The applications of the general…
A large class of first order partial nonlinear differential equations in two independent variables which possess an infinite set of polynomial conservation laws derived from an explicit generating function is constructed. The conserved…
A straightforward algorithm for the symbolic computation of higher-order symmetries of nonlinear evolution equations and lattice equations is presented. The scaling properties of the evolution or lattice equations are used to determine the…
For polynomial ODE models, we introduce and discuss the concepts of exact and approximate conservation laws, which are the first integrals of the full and truncated sets of ODEs. For fast-slow systems, truncated ODEs describe the fast…
We present direct methods and symbolic software for the computation of conservation laws of nonlinear partial differential equations (PDEs) and differential-difference equations (DDEs).The methods are applied to nonlinear PDEs in (1+1)…
An effective algorithmic method is presented for finding the local conservation laws for partial differential equations with any number of independent and dependent variables. The method does not require the use or existence of a…
This paper presents recent work on connections between symmetries and conservation laws. After reviewing Noether's theorem and its limitations, we present the Direct Construction Method to show how to find directly the conservation laws for…
The paper compares computational aspects of four approaches to compute conservation laws of single differential equations (DEs) or systems of them, ODEs and PDEs. The only restriction, required by two of the four corresponding computer…
Methods for the computation of invariants and symmetries of nonlinear evolution, wave, and lattice equations are presented. The algorithms are based on dimensional analysis, and can be implemented in any symbolic language, such as…
Conservation laws are formulated for systems of differential equations by using symmetries and adjoint symmetries, and an application to systems of evolution equations is made, together with illustrative examples. The formulation does not…