scholarly journals Solitary-wave solutions to Boussinesq systems with large surface tension

2010 ◽  
Vol 26 (4) ◽  
pp. 1153-1184 ◽  
Author(s):  
Min Chen ◽  
◽  
Nghiem V. Nguyen ◽  
Shu-Ming Sun ◽  
◽  
...  
Keyword(s):  
Surface Tension ◽  
Solitary Wave ◽  
Solitary Wave Solutions ◽  
Wave Solutions ◽  
Boussinesq Systems

Bifurcations of Traveling Wave Solutions for Fully Nonlinear Water Waves with Surface Tension in the Generalized Serre–Green–Naghdi Equations

2020 ◽  
Vol 30 (01) ◽  
pp. 2050019
Author(s):  
Jibin Li ◽  
Guanrong Chen ◽  
Jie Song
Keyword(s):  
Surface Tension ◽  
Solitary Wave ◽  
Traveling Wave ◽  
Water Waves ◽  
Traveling Wave Solutions ◽  
Wave Theory ◽  
Solitary Wave Solutions ◽  
Nonlinear Water Waves ◽  
Fully Nonlinear ◽  
Wave Solutions

For the generalized Serre–Green–Naghdi equations with surface tension, using the methodologies of dynamical systems and singular traveling wave theory developed by Li and Chen [2007] for their traveling wave systems, in different parameter conditions of the parameter space, all possible bounded solutions (solitary wave solutions, kink wave solutions, peakons, pseudo-peakons and periodic peakons as well as compactons) are obtained. More than 26 explicit exact parametric representations are given. It is interesting to find that this fully nonlinear water waves equation coexists with uncountably infinitely many smooth solitary wave solutions or infinitely many pseudo-peakon solutions with periodic solutions or compacton solutions. Differing from the well-known peakon solution of the Camassa–Holm equation, the generalized Serre–Green–Naghdi equations have four new forms of peakon solutions.

scholarly journals On solitary-wave solutions of Boussinesq/Boussinesq systems for internal waves

2021 ◽  
Vol 428 ◽  
pp. 133051
Author(s):  
Vassilios A. Dougalis ◽  
Angel Durán ◽  
Leetha Saridaki
Keyword(s):  
Solitary Wave ◽  
Internal Waves ◽  
Solitary Wave Solutions ◽  
Wave Solutions ◽  
Boussinesq Systems

scholarly journals Construction of new solitary wave solutions of generalized Zakharov-Kuznetsov-Benjamin-Bona-Mahony and simplified modified form of Camassa-Holm equations

Open Physics ◽  
2018 ◽  
Vol 16 (1) ◽  
pp. 896-909 ◽  
Author(s):  
Dianchen Lu ◽  
Aly R. Seadawy ◽  
Mujahid Iqbal
Keyword(s):  
Solitary Wave ◽  
Nonlinear Partial Differential Equations ◽  
Research Work ◽  
Traveling Wave Solutions ◽  
Elliptic Functions ◽  
Mapping Method ◽  
New Method ◽  
Auxiliary Equation ◽  
Solitary Wave Solutions ◽  
Wave Solutions

AbstractIn this research work, for the first time we introduced and described the new method, which is modified extended auxiliary equation mapping method. We investigated the new exact traveling and families of solitary wave solutions of two well-known nonlinear evaluation equations, which are generalized Zakharov-Kuznetsov-Benjamin-Bona-Mahony and simplified modified forms of Camassa-Holm equations. We used a new technique and we successfully obtained the new families of solitary wave solutions. As a result, these new solutions are obtained in the form of elliptic functions, trigonometric functions, kink and antikink solitons, bright and dark solitons, periodic solitary wave and traveling wave solutions. These new solutions show the power and fruitfulness of this new method. We can solve other nonlinear partial differential equations with the use of this method.

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