scholarly journals Solitary wave solutions to the Isobe‐Kakinuma model for water waves

2020 ◽  
Vol 145 (1) ◽  
pp. 52-80
Author(s):  
Mathieu Colin ◽  
Tatsuo Iguchi
Keyword(s):  
Solitary Wave ◽  
Water Waves ◽  
Solitary Wave Solutions ◽  
Wave 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.

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

scholarly journals A global investigation of solitary-wave solutions to a two-parameter model for water waves

1997 ◽  
Vol 342 ◽  
pp. 199-229 ◽  
Author(s):  
ALAN R. CHAMPNEYS ◽  
MARK D. GROVES
Keyword(s):  
Solitary Wave ◽  
Solitary Waves ◽  
Water Waves ◽  
Water Wave ◽  
Model Equation ◽  
Global Bifurcation ◽  
Solitary Wave Solutions ◽  
Wave Problem ◽  
Water Wave Problem ◽  
Wave Solutions

The model equationformula herearises as the equation for solitary-wave solutions to a fifth-order long-wave equation for gravity–capillary water waves. Being Hamiltonian, reversible and depending upon two parameters, it shares the structure of the full steady water-wave problem. Moreover, all known analytical results for local bifurcations of solitary-wave solutions to the full water-wave problem have precise counterparts for the model equation.At the time of writing two major open problems for steady water waves are attracting particular attention. The first concerns the possible existence of solitary waves of elevation as local bifurcation phenomena in a particular parameter regime; the second, larger, issue is the determination of the global bifurcation picture for solitary waves. Given that the above equation is a good model for solitary waves of depression, it seems natural to study the above issues for this equation; they are comprehensively treated in this article.The equation is found to have branches of solitary waves of elevation bifurcating from the trivial solution in the appropriate parameter regime, one of which is described by an explicit solution. Numerical and analytical investigations reveal a rich global bifurcation picture including multi-modal solitary waves of elevation and depression together with interactions between the two types of wave. There are also new orbit-flip bifurcations and associated multi-crested solitary waves with non-oscillatory tails.

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