Symmetry reductions and exact solutions of shallow water wave equations

1995 ◽  
Vol 39 (1-3) ◽  
pp. 245-276 ◽  
Author(s):  
Petter A. Clarkson ◽  
Elizabeth L. Mansfield
Keyword(s):  
Exact Solutions ◽  
Shallow Water ◽  
Water Wave ◽  
Wave Equations ◽  
Shallow Water Wave ◽  
Symmetry Reductions ◽  
Shallow Water Wave Equations

Symmetry Reductions and Exact Solutions of Shallow Water Wave Equations

KdV ’95 ◽  
1995 ◽  
pp. 245-276
Author(s):  
Petter A. Clarkson ◽  
Elizabeth L. Mansfield
Keyword(s):  
Exact Solutions ◽  
Shallow Water ◽  
Water Wave ◽  
Wave Equations ◽  
Shallow Water Wave ◽  
Symmetry Reductions ◽  
Shallow Water Wave Equations

Some exact solutions to the nonlinear shallow-water wave equations

1981 ◽  
Vol 107 (-1) ◽  
pp. 499 ◽  
Author(s):  
William Carlisle Thacker
Keyword(s):  
Exact Solutions ◽  
Shallow Water ◽  
Water Wave ◽  
Wave Equations ◽  
Shallow Water Wave ◽  
Shallow Water Wave Equations

New integrable (2+1)- and (3+1)-dimensional shallow water wave equations: multiple soliton solutions and lump solutions

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Abdul-Majid Wazwaz
Keyword(s):  
Shallow Water ◽  
Water Wave ◽  
Wave Equations ◽  
Soliton Solutions ◽  
Lump Solutions ◽  
Content Type ◽  
Shallow Water Wave ◽  
Multiple Soliton Solutions ◽  
Simplified Hirota’S Method ◽  
Shallow Water Wave Equations

Purpose This study aims to develop two integrable shallow water wave equations, of higher-dimensions, and with constant and time-dependent coefficients, respectively. The author derives multiple soliton solutions and a class of lump solutions which are rationally localized in all directions in space. Design/methodology/approach The author uses the simplified Hirota’s method and lump technique for determining multiple soliton solutions and lump solutions as well. The author shows that the developed (2+1)- and (3+1)-dimensional models are completely integrable in in the Painlené sense. Findings The paper reports new Painlevé-integrable extended equations which belong to the shallow water wave medium. Research limitations/implications The author addresses the integrability features of this model via using the Painlevé analysis. The author reports multiple soliton solutions for this equation by using the simplified Hirota’s method. Practical implications The obtained lump solutions include free parameters; some parameters are related to the translation invariance and the other parameters satisfy a non-zero determinant condition. Social implications The work presents useful algorithms for constructing new integrable equations and for the determination of lump solutions. Originality/value The paper presents an original work with newly developed integrable equations and shows useful findings of solitary waves and lump solutions.

Coupled shallow water wave equations

2021 ◽  
pp. 45-55
Author(s):  
P. Karunakar ◽  
Snehashish Chakraverty
Keyword(s):  
Shallow Water ◽  
Water Wave ◽  
Wave Equations ◽  
Shallow Water Wave ◽  
Shallow Water Wave Equations
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