scholarly journals Some New Nonlinear Wave Solutions for a Higher-Dimensional Shallow Water Wave Equation

2020 ◽  
Vol 08 (09) ◽  
pp. 1845-1860
Author(s):  
Longmin Dong ◽  
Zhu Guo ◽  
Yinghui He
Keyword(s):  
Wave Equation ◽  
Shallow Water ◽  
Nonlinear Wave ◽  
Water Wave ◽  
Shallow Water Wave ◽  
Wave Solutions ◽  
Higher Dimensional ◽  
Nonlinear Wave Solutions

scholarly journals Diversity of Interaction Solutions of a Shallow Water Wave Equation

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-6
Author(s):  
Jian-Ping Yu ◽  
Wen-Xiu Ma ◽  
Bo Ren ◽  
Yong-Li Sun ◽  
Chaudry Masood Khalique
Keyword(s):  
Fluid Dynamics ◽  
Wave Equation ◽  
General Theory ◽  
Shallow Water ◽  
Water Wave ◽  
Direct Method ◽  
Soliton Solutions ◽  
Interaction Solutions ◽  
Shallow Water Wave ◽  
Wave Solutions

In this paper, we study the diversity of interaction solutions of a shallow water wave equation, the generalized Hirota–Satsuma–Ito (gHSI) equation. Using the Hirota direct method, we establish a general theory for the diversity of interaction solutions, which can be applied to generate many important solutions, such as lumps and lump-soliton solutions. This is an interesting feature of this research. In addition, we prove this new model is integrable in Painlevé sense. Finally, the diversity of interactive wave solutions of the gHSI is graphically displayed by selecting specific parameters. All the obtained results can be applied to the research of fluid dynamics.

Exact travelling wave solutions for the generalized shallow water wave equation

2003 ◽  
Vol 17 (1) ◽  
pp. 121-126 ◽  
Author(s):  
S.A. Elwakil ◽  
S.K. El-labany ◽  
M.A. Zahran ◽  
R. Sabry
Keyword(s):  
Wave Equation ◽  
Shallow Water ◽  
Water Wave ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Shallow Water Wave ◽  
Wave Solutions

Dynamic interaction of behaviors of time-fractional shallow water wave equation system

2021 ◽  
pp. 2150353
Author(s):  
Serbay Duran
Keyword(s):  
Wave Equation ◽  
Shallow Water ◽  
Traveling Wave ◽  
Water Wave ◽  
Traveling Wave Solutions ◽  
Equation System ◽  
Wave Transformation ◽  
Trigonometric Functions ◽  
Shallow Water Wave ◽  
Wave Solutions

In this study, the traveling wave solutions for the time-fractional shallow water wave equation system, whose physical application is defined as the dynamics of water bodies in the ocean or seas, are investigated by [Formula: see text]-expansion method. The nonlinear fractional partial differential equation is transformed to the non-fractional ordinary differential equation with the use of a special wave transformation. In this special wave transformation, we consider the conformable fractional derivative operator to which the chain rule is applied. We obtain complex hyperbolic and complex trigonometric functions for the time-fractional shallow water wave equation system with the help of this technique. New traveling wave solutions are obtained for the special values given to the parameters in these complex hyperbolic and complex trigonometric functions, and the behavior of these solutions is examined with the help of 3D and 2D graphics.

scholarly journals Lie Symmetry Analysis and New Exact Solutions for a Higher-Dimensional Shallow Water Wave Equation

2015 ◽  
Vol 2015 ◽  
pp. 1-10
Author(s):  
Yinghui He
Keyword(s):  
Wave Equation ◽  
Shallow Water ◽  
Elliptic Function ◽  
Water Wave ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Hyperbolic Function ◽  
Lie Symmetry Analysis ◽  
Shallow Water Wave ◽  
Higher Dimensional

In our work, a higher-dimensional shallow water wave equation, which can be reduced to the potential KdV equation, is discussed. By using the Lie symmetry analysis, all of the geometric vector fields of the equation are obtained; the symmetry reductions are also presented. Some new nonlinear wave solutions, involving differentiable arbitrary functions, expressed by Jacobi elliptic function, Weierstrass elliptic function, hyperbolic function, and trigonometric function are obtained. Our work extends pioneer results.

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