In this paper, an algorithm is presented to find exact polynomial solutions of nonlinear differential-difference equations(DDEs) in terms of the Jacobi elliptic functions. The key steps of the algorithm are illustrated by the discretized mKdV lattice. A Maple package JACOBI is developed based on the
Use of symbolic computation to generate evolution equations and asymptotic solutions to elliptic equations
β Scribed by Robert W Atherton; George M Homsy
- Publisher
- Elsevier Science
- Year
- 1973
- Tongue
- English
- Weight
- 687 KB
- Volume
- 13
- Category
- Article
- ISSN
- 0021-9991
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## Abstract The convergence of the Galerkin approximations to solutions of abstract evolution equations of the form __u__β²(__t__)= β __Au__(__t__) + __M__(__u__(__t__)) is shown. Here __A__ is a closed, positive definite, selfβadjoint linear operator with domain __D__(__A__) dense in a Hilbert spac
The aim of this paper is to investigate the behaviour as tP R of solutions to the Cauchy problem , where '0 is a fixed constant, t\*0, x31L. First, we prove that if u is the solution to the linearized equation, i.e. with β’ F(u),0, then u decays like a solution for the analogous problem to the heat