scholarly journals Symbolic Computation of Conserved Densities for Systems of Nonlinear Evolution Equations

1997 ◽  
Vol 24 (5) ◽  
pp. 591-622 ◽  
Author(s):  
Ünal Göktaş ◽  
Willy Hereman
Keyword(s):  
Symbolic Computation ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Evolution Equations

Jacobi Elliptic Function Rational Expansion Method with Symbolic Computation to Construct New Doubly-periodic Solutions of Nonlinear Evolution Equations

2004 ◽  
Vol 59 (9) ◽  
pp. 529-536 ◽  
Author(s):  
Yong Chen ◽  
Qi Wang ◽  
Biao Lic
Keyword(s):  
Periodic Solutions ◽  
Symbolic Computation ◽  
Elliptic Function ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Elliptic Functions ◽  
Expansion Method ◽  
Nonlinear Evolution Equations ◽  
Jacobi Elliptic Function ◽  
Rational Form

A new Jacobi elliptic function rational expansion method is presented by means of a new general ansatz and is very powerful, with aid of symbolic computation, to uniformly construct more new exact doubly-periodic solutions in terms of rational form Jacobi elliptic function of nonlinear evolution equations (NLEEs). We choose a (2+1)-dimensional dispersive long wave equation to illustrate the method. As a result, we obtain the solutions found by most existing Jacobi elliptic function expansion methods and find other new and more general solutions at the same time. When the modulus of the Jacobi elliptic functions m→1 or 0, the corresponding solitary wave solutions and trigonometric function (singly periodic) solutions are also found.

Auto-Bäcklund Transformation and Solitary-wave Solutions to Non- integrable Generalized Fifth-order Nonlinear Evolution Equations

1999 ◽  
Vol 54 (8-9) ◽  
pp. 549-553 ◽  
Author(s):  
Woo-Pyo Hong ◽  
Young-Dae Jung
Keyword(s):  
Solitary Wave ◽  
Symbolic Computation ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Evolution Equations ◽  
Solitary Wave Solutions ◽  
New Class ◽  
Wave Solutions ◽  
Fifth Order ◽  
Truncated Painlevé Expansion

We show that the application of the truncated Painlevé expansion and symbolic computation leads to a new class of analytical solitary-wave solutions to the general fifth-order nonlinear evolution equations which include Lax, Sawada-Kotera (SK), Kaup-Kupershmidt (KK), and Ito equations. Some explicit solitary-wave solutions are presented.

ON A VARIABLE-COEFFICIENT MODIFIED KP EQUATION AND A GENERALIZED VARIABLE-COEFFICIENT KP EQUATION WITH COMPUTERIZED SYMBOLIC COMPUTATION

2001 ◽  
Vol 12 (06) ◽  
pp. 819-833 ◽  
Author(s):  
YI-TIAN GAO ◽  
BO TIAN
Keyword(s):  
Symbolic Computation ◽  
Variable Coefficient ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Analytic Solutions ◽  
Nonlinear Evolution Equations ◽  
Hyperbolic Function ◽  
Kp Equation ◽  
Exact Analytic Solutions ◽  
Hyperbolic Function Method

The variable-coefficient nonlinear evolution equations, although realistically modeling various mechanical and physical situations, often cause some well-known powerful methods not to work efficiently. In this paper, we extend the power of the generalized hyperbolic-function method, which is based on the computerized symbolic computation, to a variable-coefficient modified Kadomtsev–Petviashvili (KP) equation and a generalized variable-coefficient KP equation. New exact analytic solutions thus come out.

scholarly journals New Soliton-like Solutions of Variable Coefficient Nonlinear Schrödinger Equations

2004 ◽  
Vol 59 (4-5) ◽  
pp. 196-202 ◽  
Author(s):  
Heng-Nong Xuan ◽  
Changji Wang ◽  
Dafang Zhang
Keyword(s):  
Exact Solutions ◽  
Symbolic Computation ◽  
Variable Coefficient ◽  
Schrodinger Equation ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Evolution Equations ◽  
Nonlinear Schrödinger ◽  
System Method ◽  
Nonlinear Schrodinger Equations

The improved projective Riccati system method for solving nonlinear evolution equations (NEEs) is established. With the help of symbolic computation, one can obtain more exact solutions of some NEEs. To illustrate the method, we take the variable coefficient nonlinear Schrödinger equation as an example, and obtain four families of soliton-like solutions. Eight figures are given to illustrate some features of these solutions.

Notiz: A Symbolic Computation-Based Method and Two Nonlinear Evolution Equations for Water Waves

1997 ◽  
Vol 52 (3) ◽  
pp. 295-296
Author(s):  
Yi-Tian Gao ◽  
Bo Tian
Keyword(s):  
Symbolic Computation ◽  
Solitary Waves ◽  
Water Waves ◽  
Water Wave ◽  
Wave Equations ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Evolution Equations ◽  
Long Wave ◽  
Shallow Water Wave Equations

Abstract A symbolic-computation-based method, which has been newly proposed, is considered for a (2+1)-dimensional generalization of shallow water wave equations and a coupled set of the (2 +1)-dimensional integrable dispersive long wave equations. New sets of soliton-like solutions are constructed, along with solitary waves.

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