New Traveling Wave Solutions of the Boussinesq Equation Using a New Generalized Mapping Method

2013 ◽  
Vol 2 (2) ◽  
pp. 68-77 ◽  
Author(s):  
Xuegang Hu ◽  
Yong Hong Wu ◽  
Ling Li
Keyword(s):  
Traveling Wave ◽  
Boussinesq Equation ◽  
Traveling Wave Solutions ◽  
Mapping Method ◽  
Wave Solutions

Some Traveling Wave Solutions for the Boussinesq Equation

2011 ◽  
Vol 403-408 ◽  
pp. 196-201
Author(s):  
Qing Hua Feng ◽  
Chuan Bao Wen
Keyword(s):  
Exact Solutions ◽  
Traveling Wave ◽  
Boussinesq Equation ◽  
Traveling Wave Solutions ◽  
Exact Traveling Wave Solutions ◽  
Wave Solutions ◽  
Ode Method

In this paper, a generalized sub-ODE method is pro-posed to construct exact solutions of Boussinesq equation. As a result, some new exact traveling wave solutions are found.

Data Processing in Abound Solutions of (2 + 1)-dimensional Boussinesq Equation

2014 ◽  
Vol 1056 ◽  
pp. 215-220
Author(s):  
Han Kun Gong ◽  
Xiao Shan Zhao ◽  
Guan Hua Zhao
Keyword(s):  
Data Processing ◽  
Exact Solutions ◽  
Periodic Solutions ◽  
Symbolic Computation ◽  
Traveling Wave ◽  
Function Method ◽  
Boussinesq Equation ◽  
Traveling Wave Solutions ◽  
Wave Solutions ◽  
Solitary Solutions

In this paper, the repeated exp-function method is applied to construct exact traveling wave solutions of the (2+1)-dimensional Boussinesq equation. With aid of symbolic computation, many generalized solitary solutions, periodic solutions and other exact solutions are successfully obtained. Thus, it is proved that the method is straightforward and effective to solve the nonlinear evolutions equations.

NEW TRAVELING WAVE SOLUTIONS FOR A CLASS OF NONLINEAR EVOLUTION EQUATIONS

2011 ◽  
Vol 25 (02) ◽  
pp. 319-327 ◽  
Author(s):  
CHENG-JIE BAI ◽  
HONG ZHAO ◽  
HENG-YING XU ◽  
XIA ZHANG
Keyword(s):  
Traveling Wave ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Traveling Wave Solutions ◽  
Mapping Method ◽  
Nonlinear Evolution Equations ◽  
Wave Solutions ◽  
Trigonometric Function Solutions ◽  
Klein Gordon ◽  
Transformation Relation

The deformation mapping method is extended to solve a class of nonlinear evolution equations (NLEEs). Many types of explicit and exact traveling wave solutions, which contain solitary wave solutions, trigonometric function solutions, and Jacobian elliptic function solutions, are obtained by a simple algebraic transformation relation between the solutions of the NLEEs and those of the cubic nonlinear Klein–Gordon (NKG) equation.

scholarly journals Symmetries, Traveling Wave Solutions, and Conservation Laws of a(3+1)-Dimensional Boussinesq Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Letlhogonolo Daddy Moleleki ◽  
Chaudry Masood Khalique
Keyword(s):  
Conservation Laws ◽  
Traveling Wave ◽  
Boussinesq Equation ◽  
Traveling Wave Solutions ◽  
Lie Symmetry ◽  
Lie Symmetry Method ◽  
Wave Solutions ◽  
Simplest Equation Method ◽  
Symmetry Method ◽  
Conservation Theorem

We analyze the(3+1)-dimensional Boussinesq equation, which has applications in fluid mechanics. We find exact solutions of the(3+1)-dimensional Boussinesq equation by utilizing the Lie symmetry method along with the simplest equation method. The solutions obtained are traveling wave solutions. Moreover, we construct the conservation laws of the(3+1)-dimensional Boussinesq equation using the new conservation theorem, which is due to Ibragimov.

scholarly journals Exact Solutions to the (2+1)-Dimensional Boussinesq Equation via exp(?(?))-Expansion Method

2015 ◽  
Vol 7 (3) ◽  
pp. 1-10 ◽  
Author(s):  
M. N. Alam ◽  
M. G. Hafez ◽  
M. A. Akbar ◽  
H. -O. -Roshid
Keyword(s):  
Traveling Wave ◽  
Evolution Equations ◽  
Boussinesq Equation ◽  
Nonlinear Evolution ◽  
Traveling Wave Solutions ◽  
Rational Functions ◽  
Expansion Method ◽  
Mathematical Physics ◽  
Nonlinear Evolution Equations ◽  
Wave Solutions

The exp(?(?))-expansion method is applied to find exact traveling wave solutions to the (2+1)-dimensional Boussinesq equation which is an important equation in mathematical physics. The traveling wave solutions are expressed in terms of the exponential functions, the hyperbolic functions, the trigonometric functions and the rational functions. The procedure is simple, direct and constructive without the help of a computer algebra system. The applied method will be used in further works to establish more new solutions for other kinds of nonlinear evolution equations arising in mathematical physics and engineering.

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