Painlev$$\acute{\mathrm{e}}$$ integrable condition, auto-Bäcklund transformations, Lax pair, breather, lump-periodic-wave and kink-wave solutions of a (3+1)-dimensional Hirota–Satsuma–Ito-like system for the shallow water waves

2021 ◽  
Vol 106 (1) ◽  
pp. 765-773
Author(s):  
Yu-Qi Chen ◽  
Bo Tian ◽  
Qi-Xing Qu ◽  
Yan Sun ◽  
Su-Su Chen ◽  
...  
Keyword(s):  
Shallow Water ◽  
Water Waves ◽  
Periodic Wave ◽  
Lax Pair ◽  
Bäcklund Transformations ◽  
Shallow Water Waves ◽  
Wave Solutions ◽  
Backlund Transformations ◽  
Kink Wave

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.

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.

Characteristic of the algebraic traveling wave solutions for two extended (2 + 1)-dimensional Kadomtsev–Petviashvili equations

2019 ◽  
Vol 35 (07) ◽  
pp. 2050028 ◽  
Author(s):  
Jian-Gen Liu ◽  
Xiao-Jun Yang ◽  
Yi-Ying Feng
Keyword(s):  
Shallow Water ◽  
Traveling Wave ◽  
Water Waves ◽  
Traveling Wave Solutions ◽  
Rational Solutions ◽  
Shallow Water Waves ◽  
Weakly Nonlinear ◽  
Wave Solutions ◽  
Restoring Forces ◽  
First Time

With the aid of the planar dynamical systems and invariant algebraic cure, all algebraic traveling wave solutions for two extended (2 + 1)-dimensional Kadomtsev–Petviashvili equations, which can be used to model shallow water waves with weakly nonlinear restoring forces and to describe waves in ferromagnetic media, were obtained. Meanwhile, some new rational solutions are also yielded through an invariant algebraic cure with two different traveling wave transformations for the first time. These results are an effective complement to existing knowledge. It can help us understand the mechanism of shallow water waves more deeply.

Sign in / Sign up

Export Citation Format

Share Document