Symmetry Reductions and Integrability for the Modified Boussinesq Equation from EPU Problem

1998 ◽  
Vol 29 (1) ◽  
pp. 153-156 ◽  
Author(s):  
Qu Changzheng
Keyword(s):  
Boussinesq Equation ◽  
Symmetry Reductions ◽  
Modified Boussinesq Equation

RATIONAL SOLUTIONS OF THE BOUSSINESQ EQUATION

2008 ◽  
Vol 06 (04) ◽  
pp. 349-369 ◽  
Author(s):  
PETER A. CLARKSON
Keyword(s):  
Infinite Number ◽  
Boussinesq Equation ◽  
Nonlinear Schrödinger Equations ◽  
Schrödinger Equations ◽  
Rational Solutions ◽  
Painleve Equations ◽  
Special Polynomials ◽  
Symmetry Reductions ◽  
Nonlinear Schrodinger Equations ◽  
De Vries

Rational solutions of the Boussinesq equation are expressed in terms of special polynomials associated with rational solutions of the second and fourth Painlevé equations, which arise as symmetry reductions of the Boussinesq equation. Further generalized rational solutions of the Boussinesq equation, which involve an infinite number of arbitrary constants, are derived. The generalized rational solutions are analogs of such solutions for the Korteweg–de Vries and nonlinear Schrödinger equations.

scholarly journals An application of the MEFM to the modified Boussinesq equation

2018 ◽  
Vol 9 (1) ◽  
pp. 11-17
Author(s):  
Tolga Akturk
Keyword(s):  
Function Method ◽  
Boussinesq Equation ◽  
Travelling Wave ◽  
3D Graphics ◽  
Travelling Wave Solutions ◽  
Trigonometric Functions ◽  
Wolfram Mathematica ◽  
Modified Boussinesq Equation ◽  
Mathematica Software ◽  
2D And 3D

In this paper, some travelling wave solutions of the Modified Boussinesq (MBQ) equation are obtained by using the modified expansion function method (MEFM). When the obtained solutions are commented, trigonometric functions including hyperbolic features are obtained. The 2D and 3D graphics of the solutions have been investigated by selecting appropriate parameters. All the obtained solutions provide the MBQ equation. In this work, all mathematical calculations are done with Wolfram Mathematica software. 

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