scholarly journals Solitary wave solutions and their interactions for fully nonlinear water waves with surface tension in the generalized Serre equations

2018 ◽  
Vol 32 (3) ◽  
pp. 371-397 ◽  
Author(s):  
Denys Dutykh ◽  
Mark Hoefer ◽  
Dimitrios Mitsotakis
Keyword(s):  
Surface Tension ◽  
Solitary Wave ◽  
Water Waves ◽  
Solitary Wave Solutions ◽  
Nonlinear Water Waves ◽  
Fully Nonlinear ◽  
Wave Solutions

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 Gaussian solitary waves to Boussinesq equation with dual dispersion and logarithmic nonlinearity

2018 ◽  
Vol 23 (6) ◽  
pp. 942-950 ◽  
Author(s):  
Anjan Biswasa ◽  
Mehmet Ekici ◽  
Abdullah Sonmezoglu
Keyword(s):  
Solitary Wave ◽  
Shallow Water ◽  
Solitary Waves ◽  
Water Waves ◽  
Trial Function ◽  
Boussinesq Equation ◽  
Solitary Wave Solutions ◽  
Shallow Water Waves ◽  
Wave Solutions ◽  
Extended Trial

This paper discusses shallow water waves that is modeled with Boussinesq equation that comes with dual dispersion and logarithmic nonlinearity. The extended trial function scheme retrieves exact Gaussian solitary wave solutions to the model.

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

Exact and explicit solitary wave solutions to a model equation for water waves

1989 ◽  
Vol 139 (8) ◽  
pp. 373-374 ◽  
Author(s):  
Guo-xiang Huang ◽  
Sen-yue Luo ◽  
Xian-xi Dai
Keyword(s):  
Solitary Wave ◽  
Water Waves ◽  
Model Equation ◽  
Solitary Wave Solutions ◽  
Wave Solutions
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