Travelling wave solutions to Zufiria’s higher-order Boussinesq type equations

2009 ◽  
Vol 71 (12) ◽  
pp. e711-e724 ◽  
Author(s):  
Liang Gao ◽  
Wen-Xiu Ma ◽  
Wei Xu
Keyword(s):  
Travelling Wave ◽  
Higher Order ◽  
Travelling Wave Solutions ◽  
Wave Solutions

scholarly journals Travelling Wave Solutions to the Benney-Luke and the Higher-Order Improved Boussinesq Equations of Sobolev Type

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Ömer Faruk Gözükızıl ◽  
Şamil Akçağıl
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Boussinesq Equation ◽  
Boussinesq Equations ◽  
Travelling Wave ◽  
Higher Order ◽  
Sobolev Type ◽  
Travelling Wave Solutions ◽  
Partial Differential ◽  
Wave Solutions

By using the tanh-coth method, we obtained some travelling wave solutions of two well-known nonlinear Sobolev type partial differential equations, namely, the Benney-Luke equation and the higher-order improved Boussinesq equation. We show that the tanh-coth method is a useful, reliable, and concise method to solve these types of equations.

scholarly journals New exact soliton solutions, bifurcation and multistability behaviors of traveling waves for the (3+1)-dimensional modified Zakharov-Kuznetsov equation with higher order dispersion

2021 ◽  
Author(s):  
Asit Saha ◽  
Battal Gazi Karakoç ◽  
Khalid K. Ali
Keyword(s):  
Traveling Wave ◽  
Soliton Solutions ◽  
Travelling Wave ◽  
Higher Order ◽  
Physical Parameters ◽  
Travelling Wave Solutions ◽  
Wave Solutions ◽  
Higher Order Dispersion ◽  
Order Dispersion ◽  
Bifurcation Behavior

The goal of the present paper is to obtain and analyze new exact travelling wave solutions and bifurcation behavior of modified Zakharov-Kuznetsov (mZK) equation with higher order dispersion term. For this purpose, first and second simple methods are used to build soliton solutions of travelling wave solutions. Furthermore, bifurcation behavior of traveling waves including new type of quasiperiodic and multi-periodic traveling wave motions have been examined depending on the physical parameters. Multistability for the nonlinear mZK equation has been investigated depending on fixed values of physical parameters with various initial conditions. The suggested methods for the analytical solutions are powerful and benefical tools to obtain the exact travelling wave solutions of nonlinear evolution equations (NLEEs). Two and three-dimensional plots are also provided to illustrate the new solutions. Bifurcation and multistability behaviors of traveling wave solution of the nonlinear mZK equation with higher order dispersion will add some value in the literature of mathematical and plasma physics.

Integrability Test and Travelling-Wave Solutions of Higher-Order Shallow- Water Type Equations

2010 ◽  
Vol 65 (4) ◽  
pp. 353-356
Author(s):  
Mercedes Maldonado ◽  
María Celeste Molinero ◽  
Andrew Pickering ◽  
Julia Prada
Keyword(s):  
Shallow Water ◽  
Travelling Wave ◽  
Higher Order ◽  
Water Type ◽  
Travelling Wave Solutions ◽  
Compatibility Conditions ◽  
Wave Solutions

We apply the Weiss-Tabor-Carnevale (WTC) Painlev´e test to members of a sequence of higher-order shallow-water type equations. We obtain the result that the equations considered are non-integrable, although compatibility conditions at real resonances are satisfied. We also construct travelling-wave solutions for these and related equations.

scholarly journals Travelling wave solutions for higher-order wave equations of KDV type (III)

2006 ◽  
Vol 3 (1) ◽  
pp. 125-135 ◽  
Author(s):  
Jibin Li ◽  
◽  
Weigou Rui ◽  
Yao Long ◽  
Bin He ◽  
...  
Keyword(s):  
Wave Equations ◽  
Travelling Wave ◽  
Higher Order ◽  
Travelling Wave Solutions ◽  
Type Iii ◽  
Wave Solutions
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