scholarly journals New Exact Jacobi Elliptic Function Solutions for the Coupled Schrödinger-Boussinesq Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Baojian Hong ◽  
Dianchen Lu
Keyword(s):  
Elliptic Function ◽  
Nonlinear Partial Differential Equations ◽  
Boussinesq Equations ◽  
Elliptic Functions ◽  
Expansion Method ◽  
Algebraic Method ◽  
Auxiliary Function ◽  
Jacobi Elliptic Function ◽  
Deformation Method ◽  
Wave Solutions

A general algebraic method based on the generalized Jacobi elliptic functions expansion method, the improved general mapping deformation method, and the extended auxiliary function method with computerized symbolic computation is proposed to construct more new exact solutions for coupled Schrödinger-Boussinesq equations. As a result, several families of new generalized Jacobi elliptic function wave solutions are obtained by using this method, some of them are degenerated to solitary wave solutions and trigonometric function solutions in the limited cases, which shows that the general method is more powerful than plenty of traditional methods and will be used in further works to establish more entirely new solutions for other kinds of nonlinear partial differential equations arising in mathematical physics.

scholarly journals Improved General Mapping Deformation Method for Nonlinear Partial Differential Equations in Mathematical Physics

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Khaled A. Gepreel
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Elliptic Functions ◽  
Expansion Method ◽  
Mathematical Physics ◽  
Jacobi Elliptic Function ◽  
Deformation Method ◽  
Partial Differential ◽  
General Mapping

We use the improved general mapping deformation method based on the generalized Jacobi elliptic functions expansion method to construct some of the generalized Jacobi elliptic solutions for some nonlinear partial differential equations in mathematical physics via the generalized nonlinear Klein-Gordon equation and the classical Boussinesq equations. As a result, some new generalized Jacobi elliptic function-like solutions are obtained by using this method. This method is more powerful to find the exact solutions for nonlinear partial differential equations.

scholarly journals Travelling wave solutions to the proximate equations for LWSW

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
XiuQing Yu ◽  
Shuxia Kong
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Elliptic Function ◽  
Nonlinear Partial Differential Equations ◽  
Algebraic Method ◽  
Travelling Wave ◽  
Arbitrary Parameter ◽  
Jacobi Elliptic Function ◽  
Travelling Wave Solutions ◽  
Wave Solutions

Abstract By feat of Maple 17 and a subsidiary ordinary differential equation, a new extension algebraic method is chosen to construct the travelling wave solutions to the proximate equation set involving an arbitrary parameter for long waves over shallow-water. Multiple triangle periodic solutions and new Jacobi elliptic function solutions are obtained. This procedure is applicable to other nonlinear partial differential equations as well.

Analytical Solutions of Two Space-Time Fractional Nonlinear Models Using Jacobi Elliptic Function Expansion Method

2021 ◽  
pp. 173-188
Author(s):  
Zillur Rahman ◽  
M. Zulfikar Ali ◽  
Harun-Or-Roshid ◽  
Mohammad Safi Ullah
Keyword(s):  
Elliptic Function ◽  
Nonlinear Models ◽  
Applied Mathematics ◽  
Elliptic Functions ◽  
Expansion Method ◽  
Space Time ◽  
Jacobi Elliptic Function ◽  
Function Expansion ◽  
Partial Models ◽  
Jacobi Elliptic Function Expansion

In this manuscript, the space-time fractional Equal-width (s-tfEW) and the space-time fractional Wazwaz-Benjamin-Bona-Mahony (s-tfWBBM) models have been investigated which are frequently arises in nonlinear optics, solid states, fluid mechanics and shallow water. Jacobi elliptic function expansion integral technique has been used to build more innovative exact solutions of the s-tfEW and s-tfWBBM nonlinear partial models. In this research, fractional beta-derivatives are applied to convert the partial models to ordinary models. Several types of solutions have been derived for the models and performed some new solitary wave phenomena. The derived solutions have been presented in the form of Jacobi elliptic functions initially. Persevering different conditions on a parameter, we have achieved hyperbolic and trigonometric functions solutions from the Jacobi elliptic function solutions. Besides the scientific derivation of the analytical findings, the results have been illustrated graphically for clear identification of the dynamical properties. It is noticeable that the integral scheme is simplest, conventional and convenient in handling many nonlinear models arising in applied mathematics and the applied physics to derive diverse structural precise solutions.

Jacobi Elliptic Function Solutions of Three Coupled Nonlinear Physical Equations

2005 ◽  
Vol 60 (4) ◽  
pp. 237-244 ◽  
Author(s):  
M. M. Hassan ◽  
A. H. Khater
Keyword(s):  
Solitary Wave ◽  
Elliptic Function ◽  
Nonlinear Partial Differential Equations ◽  
Wave Interaction ◽  
Short Wave ◽  
Jacobi Elliptic Function ◽  
Solitary Wave Solutions ◽  
Wave Solutions ◽  
Pacs 02.30 ◽  
Limiting Case

Abstract The Jacobi elliptic function solutions of coupled nonlinear partial differential equations, including the coupled modified KdV (mKdV) equations, long-short-wave interaction system and the Davey- Stewartson (DS) equations, are obtained by using the mixed dn-sn method. The solutions obtained in this paper include the single and the combined Jacobi elliptic function solutions. In the limiting case, the solitary wave solutions of the systems are also given. - PACS: 02.30.Jr; 03.40.Kf; 03.65.Fd

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.

Elliptic Function Solutions of (2+1)-dimensional Longwave – Shortwave Resonance Interaction Equation via a sinh-Gordon Expansion Method

2004 ◽  
Vol 59 (1-2) ◽  
pp. 23-28 ◽  
Author(s):  
Zhenya Yan
Keyword(s):  
Elliptic Function ◽  
Elliptic Functions ◽  
Expansion Method ◽  
Short Wave ◽  
Resonance Interaction ◽  
Jacobi Elliptic Function ◽  
Wave Resonance ◽  
Trigonometric Function Solutions ◽  
Interaction Equation ◽  
Pacs 02.30

With the aid of symbolic computation, the sinh-Gordon equation expansion method is extended to seek Jacobi elliptic function solutions of (2+1)-dimensional long wave-short wave resonance interaction equation, which describe the long and short waves propagation at an angle to each other in a two-layer fluid. As a result, new Jacobi elliptic function solutions are obtained. When the modulus m of Jacobi elliptic functions approaches 1, we also deduce the singular oliton solutions; while when the modulus m→0, we get the trigonometric function solutions. - PACS: 02.30.Jr, 03.40.Kf

scholarly journals A New Extended Jacobi Elliptic Function Expansion Method and Its Application to the Generalized Shallow Water Wave Equation

2012 ◽  
Vol 2012 ◽  
pp. 1-21
Author(s):  
Yafeng Xiao ◽  
Haili Xue ◽  
Hongqing Zhang
Keyword(s):  
Shallow Water ◽  
Periodic Solutions ◽  
Elliptic Function ◽  
Water Wave ◽  
Expansion Method ◽  
Jacobi Elliptic Function ◽  
Shallow Water Wave ◽  
Wave Solutions ◽  
Function Expansion ◽  
Jacobi Elliptic Function Expansion

With the aid of symbolic computation, a new extended Jacobi elliptic function expansion method is presented by means of a new ansatz, in which periodic solutions of nonlinear evolution equations, which can be expressed as a finite Laurent series of some 12 Jacobi elliptic functions, are very effective to uniformly construct more new exact periodic solutions in terms of Jacobi elliptic function solutions of nonlinear partial differential equations. As an application of the method, we choose the generalized shallow water wave (GSWW) equation to illustrate the method. As a result, we can successfully obtain more new solutions. Of course, more shock wave solutions or solitary wave solutions can be gotten at their limit condition.

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.

Sign in / Sign up

Export Citation Format

Share Document