scholarly journals Study on New Doubly-periodic Solutions of two Coupled Nonlinear Wave Equations in Complex and Real Fields

2004 ◽  
Vol 59 (1-2) ◽  
pp. 29-34 ◽  
Author(s):  
Zhenya Yan
Keyword(s):  
Solitary Wave ◽  
Periodic Solutions ◽  
Nonlinear Wave ◽  
Wave Equations ◽  
Elliptic Functions ◽  
Scalar Fields ◽  
Nonlinear Wave Equations ◽  
Solitary Wave Solutions ◽  
Real Scalar ◽  
Wave Solutions

In this paper, new doubly-periodic solutions in terms of Weierstrass elliptic functions are investigated for the coupled nonlinear Schr¨odinger equation and systems of two coupled real scalar fields. Solitary wave solutions are also given as simple limits of doubly periodic solutions. - PACS: 03.40.Kf; 02.30Ik

Travelling And Periodic Wave Solutions Of Some Nonlinear Wave Equations

2004 ◽  
Vol 59 (7-8) ◽  
pp. 389-396 ◽  
Author(s):  
A. H. Khater ◽  
M. M. Hassan
Keyword(s):  
Nonlinear Wave ◽  
Wave Equations ◽  
Elliptic Functions ◽  
Periodic Wave ◽  
Travelling Wave ◽  
Nonlinear Wave Equations ◽  
Travelling Wave Solutions ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Pacs 02.30

We present the mixed dn-sn method for finding periodic wave solutions of some nonlinear wave equations. Introducing an appropriate transformation, we extend this method to a special type of nonlinear equations and construct their solutions, which are not expressible as polynomials in the Jacobi elliptic functions. The obtained solutions include the well known kink-type and bell-type solutions as a limiting cases. Also, some new travelling wave solutions are found. - PACS: 02.30.Jr; 03.40.Kf

scholarly journals Exact Solitary Wave and Periodic Wave Solutions of a Class of Higher-Order Nonlinear Wave Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Lijun Zhang ◽  
Chaudry Masood Khalique
Keyword(s):  
Solitary Wave ◽  
Nonlinear Wave ◽  
Wave Equations ◽  
Kdv Equation ◽  
Periodic Wave ◽  
Sixth Order ◽  
Nonlinear Wave Equations ◽  
Lax Equation ◽  
Periodic Wave Solutions ◽  
Wave Solutions

We study the exact traveling wave solutions of a general fifth-order nonlinear wave equation and a generalized sixth-order KdV equation. We find the solvable lower-order subequations of a general related fourth-order ordinary differential equation involving only even order derivatives and polynomial functions of the dependent variable. It is shown that the exact solitary wave and periodic wave solutions of some high-order nonlinear wave equations can be obtained easily by using this algorithm. As examples, we derive some solitary wave and periodic wave solutions of the Lax equation, the Ito equation, and a general sixth-order KdV equation.

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