scholarly journals Traveling wave solutions for shallow water equations

2017 ◽  
Vol 2 (1) ◽  
pp. 28-33 ◽  
Author(s):  
U.M. Abdelsalam
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Wave Solutions

scholarly journals Approximate Traveling Wave Solutions of Coupled Whitham-Broer-Kaup Shallow Water Equations by Homotopy Analysis Method

2008 ◽  
Vol 2008 ◽  
pp. 1-8 ◽  
Author(s):  
M. M. Rashidi ◽  
D. D. Ganji ◽  
S. Dinarvand
Keyword(s):  
Exact Solutions ◽  
Shallow Water ◽  
Homotopy Analysis Method ◽  
Shallow Water Equations ◽  
Traveling Wave ◽  
Nonlinear Partial Differential Equations ◽  
Traveling Wave Solutions ◽  
Analysis Method ◽  
Wave Solutions ◽  
Homotopy Analysis

The homotopy analysis method (HAM) is applied to obtain the approximate traveling wave solutions of the coupled Whitham-Broer-Kaup (WBK) equations in shallow water. Comparisons are made between the results of the proposed method and exact solutions. The results show that the homotopy analysis method is an attractive method in solving the systems of nonlinear partial differential equations.

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.

EXPLICIT AND EXACT NON-TRAVELING WAVE SOLUTIONS OF (3+1)-DIMENSIONAL GENERALIZED SHALLOW WATER EQUATION

2019 ◽  
Vol 9 (6) ◽  
pp. 2381-2388
Author(s):  
Jianguo Liu ◽  
◽  
Wenhui Zhu ◽  
Li Zhou ◽  
Yan He ◽  
...  
Keyword(s):  
Shallow Water ◽  
Traveling Wave ◽  
Shallow Water Equation ◽  
Traveling Wave Solutions ◽  
Wave Solutions

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.

More on Bifurcations and Dynamics of Traveling Wave Solutions for a Higher-Order Shallow Water Wave Equation

2019 ◽  
Vol 29 (01) ◽  
pp. 1950014
Author(s):  
Jibin Li ◽  
Guanrong Chen
Keyword(s):  
Shallow Water ◽  
Traveling Wave ◽  
Water Wave ◽  
Traveling Wave Solutions ◽  
Wave Model ◽  
Periodic Wave ◽  
Wave System ◽  
Shallow Water Wave ◽  
Wave Solutions ◽  
Straight Lines

This paper studies the dynamics of traveling wave solutions to a shallow water wave model with a large-amplitude regime in phase space. The corresponding traveling wave system is a singular planar dynamical system with two singular straight lines. By using the method of dynamical systems, bifurcation diagrams are obtained. The existence of solitary wave solutions, periodic wave solutions, peakon, pseudo-peakon solution, periodic peakon solutions and compacton solutions are determined under different parameter conditions.

scholarly journals Stability of Periodic, Traveling-Wave Solutions to the Capillary Whitham Equation

Fluids ◽  
2019 ◽  
Vol 4 (1) ◽  
pp. 58 ◽  
Author(s):  
John D. Carter ◽  
Morgan Rozman
Keyword(s):  
Surface Tension ◽  
Shallow Water ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Representative Sampling ◽  
Wave Speeds ◽  
Wave Solutions ◽  
Whitham Equations ◽  
Periodic Traveling Wave ◽  
Whitham Equation

Recently, the Whitham and capillary Whitham equations were shown to accurately modelthe evolution of surface waves on shallow water. In order to gain a deeper understanding of theseequations, we compute periodic, traveling-wave solutions for both and study their stability. Wepresent plots of a representative sampling of solutions for a range of wavelengths, wave speeds, waveheights, and surface tension values. Finally, we discuss the role these parameters play in the stabilityof these solutions.

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