WATER WAVE EQUATIONS

2005 ◽  
Author(s):  
JIN E. ZHANG
Keyword(s):  
Water Wave ◽  
Wave Equations

New integrable (2+1)- and (3+1)-dimensional shallow water wave equations: multiple soliton solutions and lump solutions

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Abdul-Majid Wazwaz
Keyword(s):  
Shallow Water ◽  
Water Wave ◽  
Wave Equations ◽  
Soliton Solutions ◽  
Lump Solutions ◽  
Content Type ◽  
Shallow Water Wave ◽  
Multiple Soliton Solutions ◽  
Simplified Hirota’S Method ◽  
Shallow Water Wave Equations

Purpose This study aims to develop two integrable shallow water wave equations, of higher-dimensions, and with constant and time-dependent coefficients, respectively. The author derives multiple soliton solutions and a class of lump solutions which are rationally localized in all directions in space. Design/methodology/approach The author uses the simplified Hirota’s method and lump technique for determining multiple soliton solutions and lump solutions as well. The author shows that the developed (2+1)- and (3+1)-dimensional models are completely integrable in in the Painlené sense. Findings The paper reports new Painlevé-integrable extended equations which belong to the shallow water wave medium. Research limitations/implications The author addresses the integrability features of this model via using the Painlevé analysis. The author reports multiple soliton solutions for this equation by using the simplified Hirota’s method. Practical implications The obtained lump solutions include free parameters; some parameters are related to the translation invariance and the other parameters satisfy a non-zero determinant condition. Social implications The work presents useful algorithms for constructing new integrable equations and for the determination of lump solutions. Originality/value The paper presents an original work with newly developed integrable equations and shows useful findings of solitary waves and lump solutions.

Comparison of Two Versions of the Mnls With the Full Water Wave Equations

2021 ◽  
Author(s):  
Tianning Tang ◽  
Ye Li ◽  
Harry B. Bingham ◽  
Thomas Adcock
Keyword(s):  
Water Wave ◽  
Wave Equations

scholarly journals A variety of exact analytical solutions of extended shallow water wave equations via improved (G’/G) -expansion method

2017 ◽  
Vol 5 (1) ◽  
pp. 21 ◽  
Author(s):  
Faisal Hawlader ◽  
Dipankar Kumar
Keyword(s):  
Shallow Water ◽  
Traveling Wave ◽  
Water Wave ◽  
Wave Equations ◽  
Rational Functions ◽  
Expansion Method ◽  
Arbitrary Parameter ◽  
Shallow Water Wave ◽  
Wave Solutions ◽  
Shallow Water Wave Equations

In this present work, we have established exact solutions for (2+1) and (3+1) dimensional extended shallow-water wave equations in-volving parameters by applying the improved (G’/G) -expansion method. Abundant traveling wave solutions with arbitrary parameter are successfully obtained by this method, and these wave solutions are expressed in terms of hyperbolic, trigonometric, and rational functions. The improved (G’/G) -expansion method is simple and powerful mathematical technique for constructing traveling wave, solitary wave, and periodic wave solutions of the nonlinear evaluation equations which arise from application in engineering and any other applied sciences. We also present the 3D graphical description of the obtained solutions for different cases with the aid of MAPLE 17.

scholarly journals NUMERICAL MODEL OF BREAKWATER WAVE FLOWS

1988 ◽  
Vol 1 (21) ◽  
pp. 149 ◽  
Author(s):  
Alex C. Thompson
Keyword(s):  
Mathematical Model ◽  
Numerical Model ◽  
Reflection Coefficient ◽  
Water Wave ◽  
Wave Equations ◽  
Seepage Flow ◽  
Experimental Results ◽  
Simplified Model ◽  
Flow Equations ◽  
Shallow Water Wave Equations

A mathematical model of flow on a sloping breakwater face is described and results of calculations compared with some experimental results to show how the model can be calibrated. Flow above the surface of the slope is represented by the shallow water wave equations solved by a finite difference method. Flow within the breakwater is calculated by one of two methods. A solution of the linear seepage flow equations, again using finite differences or a simplified model of inflow can be used. Experimental results for runup and reflection coefficient are from tests performed at HRL Wallingford.

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