Symmetry Reductions and Exact Solutions for a Generalised Boussinesq Equation

1993 ◽  
pp. 415-430 ◽  
Author(s):  
D. K. Ludlow ◽  
P. A. Clarkson
Keyword(s):  
Exact Solutions ◽  
Boussinesq Equation ◽  
Symmetry Reductions

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 Symmetry reductions and exact solutions of Lax integrable 3-dimensional systems

2014 ◽  
Vol 21 (4) ◽  
pp. 643-671 ◽  
Author(s):  
H. Baran ◽  
I.S. Krasil'shchik ◽  
O.I. Morozov ◽  
P. Vojčák
Keyword(s):  
Exact Solutions ◽  
3 Dimensional ◽  
Symmetry Reductions
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