Some new Jacobi elliptic function solutions for the short-pulse equation via a direct symbolic computation method

2012 ◽  
Vol 40 (1-2) ◽  
pp. 683-690 ◽  
Author(s):  
Yu-Lan Ma ◽  
Bang-Qing Li
Keyword(s):  
Symbolic Computation ◽  
Elliptic Function ◽  
Short Pulse ◽  
Computation Method ◽  
Jacobi Elliptic Function ◽  
Short Pulse Equation

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.

scholarly journals The Study of the Solution to a Generalized KdV-mKdV Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-17 ◽  
Author(s):  
Xiumei Lv ◽  
Tengwei Shao ◽  
Jiacheng Chen
Keyword(s):  
Symbolic Computation ◽  
Elliptic Function ◽  
Mkdv Equation ◽  
High Order ◽  
Auxiliary Equation ◽  
Jacobi Elliptic Function ◽  
Mathematical Technique ◽  
Triangle Function

A mathematical technique based on an auxiliary equation and the symbolic computation system Matlab is employed to investigate a generalized KdV-mKdV equation which possesses high-order nonlinear terms. Some new solutions including the Jacobi elliptic function solutions, the degenerated soliton-like solutions, and the triangle function solutions to the equation are obtained.

NEW JACOBI ELLIPTIC FUNCTION SOLUTIONS OF (2 +1)-DIMENSIONAL COMPLEX NONLINEAR INTEGRABLE SYSTEM

2003 ◽  
Vol 14 (03) ◽  
pp. 277-284 ◽  
Author(s):  
ZHENYA YAN
Keyword(s):  
Periodic Solutions ◽  
Integrable System ◽  
Symbolic Computation ◽  
Elliptic Function ◽  
Elliptic Functions ◽  
Expansion Method ◽  
Jacobi Elliptic Function ◽  
Jacobian Elliptic Functions ◽  
Jacobi Elliptic Function Expansion ◽  
Nonlinear Integrable System

Recently sixteen types of doubly-periodic solutions were obtained for the new (2 +1)-dimensional complex nonlinear integrable system. In this paper with the aid of computerized symbolic computation, our extended Jacobi elliptic function expansion method is extended to this system. As a result, another eight families of Jacobian elliptic functions solutions are also found.

Soliton resolution for the short-pulse equation

2021 ◽  
Vol 280 ◽  
pp. 644-689
Author(s):  
Yiling Yang ◽  
Engui Fan
Keyword(s):  
Short Pulse ◽  
Short Pulse Equation

Study on soliton solutions of the longitudinal wave equation and magneto-electro-elastic circular rod dynamical model

2021 ◽  
Vol 35 (13) ◽  
pp. 2150168
Author(s):  
Adel Darwish ◽  
Aly R. Seadawy ◽  
Hamdy M. Ahmed ◽  
A. L. Elbably ◽  
Mohammed F. Shehab ◽  
...  
Keyword(s):  
Wave Equation ◽  
Exact Solutions ◽  
Longitudinal Wave ◽  
Physical Interpretation ◽  
Elliptic Function ◽  
Function Method ◽  
Three Dimensional ◽  
Soliton Solutions ◽  
Jacobi Elliptic Function ◽  
Two Dimensional

In this paper, we use the improved modified extended tanh-function method to obtain exact solutions for the nonlinear longitudinal wave equation in magneto-electro-elastic circular rod. With the aid of this method, we get many exact solutions like bright and singular solitons, rational, singular periodic, hyperbolic, Jacobi elliptic function and exponential solutions. Moreover, the two-dimensional and the three-dimensional graphs of some solutions are plotted for knowing the physical interpretation.

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