A novel method for travelling wave solutions of fractional Whitham-Broer-Kaup, fractional modified Boussinesq and fractional approximate long wave equations in shallow water

2014 ◽  
Vol 38 (7) ◽  
pp. 1352-1368 ◽  
Author(s):  
S. Saha Ray
Keyword(s):  
Shallow Water ◽  
Wave Equations ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Wave Solutions ◽  
Long Wave ◽  
Novel Method

scholarly journals Travelling-Wave Solutions for Wave Equations with Two Exponential Nonlinearities

2018 ◽  
Vol 73 (10) ◽  
pp. 883-892
Author(s):  
Stefan C. Mancas ◽  
Haret C. Rosu ◽  
Maximino Pérez-Maldonado
Keyword(s):  
Dynamical Systems ◽  
Elliptic Equations ◽  
Hypergeometric Functions ◽  
Wave Equations ◽  
Constant Term ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Simple Method ◽  
Solutions Of Wave Equations ◽  
Wave Solutions

AbstractWe use a simple method that leads to the integrals involved in obtaining the travelling-wave solutions of wave equations with one and two exponential nonlinearities. When the constant term in the integrand is zero, implicit solutions in terms of hypergeometric functions are obtained, while when that term is nonzero, all the basic travelling-wave solutions of Liouville, Tzitzéica, and their variants, as as well sine/sinh-Gordon equations with important applications in the phenomenology of nonlinear physics and dynamical systems are found through a detailed study of the corresponding elliptic equations.

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

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