Construction of solitary wave solutions of some nonlinear dynamical system arising in nonlinear water wave models

2019 ◽  
Vol 94 (11) ◽  
pp. 1785-1794
Author(s):  
Aly R. Seadawy ◽  
Dianchen Lu ◽  
Naila Nasreen
Keyword(s):  
Dynamical System ◽  
Solitary Wave ◽  
Water Wave ◽  
Nonlinear Dynamical System ◽  
Solitary Wave Solutions ◽  
Nonlinear Dynamical ◽  
Wave Solutions ◽  
Wave Models

Completing the Study of Traveling Wave Solutions for Three Two-Component Shallow Water Wave Models

2020 ◽  
Vol 30 (03) ◽  
pp. 2050036 ◽  
Author(s):  
Jibin Li ◽  
Guanrong Chen ◽  
Jie Song
Keyword(s):  
Solitary Wave ◽  
Shallow Water ◽  
Traveling Wave ◽  
Water Wave ◽  
Wave System ◽  
Solitary Wave Solutions ◽  
Shallow Water Wave ◽  
Wave Solutions ◽  
Two Component ◽  
Wave Models

For three two-component shallow water wave models, from the approach of dynamical systems and the singular traveling wave theory developed in [Li & Chen, 2007], under different parameter conditions, all possible bounded solutions (solitary wave solutions, pseudo-peakons, periodic peakons, as well as smooth periodic wave solutions) are derived. More than 19 explicit exact parametric representations are obtained. Of more interest is that, for the integrable two-component generalization of the Camassa–Holm equation, it is found that its [Formula: see text]-traveling wave system has a family of pseudo-peakon wave solutions. In addition, its [Formula: see text]-traveling wave system has two families of uncountably infinitely many solitary wave solutions. The new results complete a recent study by Dutykh and Ionescu-Kruse [2016].

Exact Solitary-wave Solutions for the General Fifth-order Shallow Water-wave Models

1999 ◽  
Vol 54 (3-4) ◽  
pp. 272-274
Author(s):  
Woo-Pyo Hong ◽  
Young-Dae Jung
Keyword(s):  
Solitary Wave ◽  
Shallow Water ◽  
Symbolic Computation ◽  
Water Wave ◽  
Model Parameters ◽  
Solitary Wave Solutions ◽  
Wave Solutions ◽  
Special Cases ◽  
Wave Models ◽  
Fifth Order

We perform a computerized symbolic computation to find some general solitonic solutions for the general fifth-order shal-low water-wave models. Applying the tanh-typed method, we have found certain new exact solitary wave solutions. The pre-viously published solutions turn out to be special cases with restricted model parameters.

EXTENDED TANH-METHODS AND SOLITONIC SOLUTIONS OF THE GENERAL SHALLOW WATER WAVE MODELS

2004 ◽  
Vol 15 (03) ◽  
pp. 363-370 ◽  
Author(s):  
WOO-PYO HONG ◽  
SEOUNG-HWAN PARK
Keyword(s):  
Solitary Wave ◽  
Shallow Water ◽  
Traveling Wave ◽  
Water Wave ◽  
Traveling Wave Solutions ◽  
Solitary Wave Solutions ◽  
Shallow Water Wave ◽  
Wave Solutions ◽  
Wave Models

Based on the two recent extended tanh-function methods, we find traveling-wave solutions for the general shallow water wave models. The obtained solutions include periodical, singular and solitary-wave solutions.

scholarly journals Time Evolution of Folded (2+1)-Dimensional Solitary Waves

2009 ◽  
Vol 64 (5-6) ◽  
pp. 309-314 ◽  
Author(s):  
Song-Hua Ma ◽  
Yi-Pin Lu ◽  
Jian-Ping Fang ◽  
Zhi-Jie Lv
Keyword(s):  
Solitary Wave ◽  
Elliptic Function ◽  
Water Wave ◽  
Periodic Wave ◽  
Wave System ◽  
Solitary Wave Solutions ◽  
Variable Separation ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Variable Separation Approach

Abstract With an extended mapping approach and a linear variable separation approach, a series of solutions (including theWeierstrass elliptic function solutions, solitary wave solutions, periodic wave solutions and rational function solutions) of the (2+1)-dimensional modified dispersive water-wave system (MDWW) is derived. Based on the derived solutions and using some multi-valued functions, we find a few new folded solitary wave excitations.

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