scholarly journals Dynamical behaviour of shallow water waves and solitary wave solutions of the Dullin-Gottwald-Holm dynamical system

2021 ◽  
pp. 101627
Author(s):  
M.H. Raddadi ◽  
M. Younis ◽  
Aly R. Seadawy ◽  
S.U. Rehman ◽  
M. Bilal ◽  
...  
Keyword(s):  
Dynamical System ◽  
Solitary Wave ◽  
Shallow Water ◽  
Water Waves ◽  
Dynamical Behaviour ◽  
Solitary Wave Solutions ◽  
Shallow Water Waves ◽  
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.

Three-Dimensional Weakly Nonlinear Shallow Water Waves Regime and its Traveling Wave Solutions

2018 ◽  
Vol 15 (03) ◽  
pp. 1850017 ◽  
Author(s):  
Aly R. Seadawy
Keyword(s):  
Free Surface ◽  
Solitary Wave ◽  
Shallow Water ◽  
Traveling Wave ◽  
Water Waves ◽  
Three Dimensional ◽  
Traveling Wave Solutions ◽  
Shallow Water Waves ◽  
Weakly Nonlinear ◽  
Wave Solutions

The problem formulations of models for three-dimensional weakly nonlinear shallow water waves regime in a stratified shear flow with a free surface are studied. Traveling wave solutions are generated by deriving the nonlinear higher order of nonlinear evaluation equations for the free surface displacement. We obtain the velocity potential and pressure fluid in the form of traveling wave solutions of the obtained nonlinear evaluation equation. The obtained solutions and the movement role of the waves of the exact solutions are new travelling wave solutions in different and explicit form such as solutions (bright and dark), solitary wave, periodic solitary wave elliptic function solutions of higher-order nonlinear evaluation equation.

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].

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