scholarly journals Physically significant wave solutions to the Riemann wave equations and the Landau-Ginsburg-Higgs equation

2021 ◽  
pp. 104517
Author(s):  
Hemonta Kumar Barman ◽  
Most. Shewly Aktar ◽  
M. Hafiz Uddin ◽  
M. Ali Akbar ◽  
Dumitru Baleanu ◽  
...  
Keyword(s):  
Wave Equations ◽  
Significant Wave ◽  
Riemann Wave ◽  
Wave Solutions

The twin properties of rogue waves and homoclinic solutions for some nonlinear wave equations

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Wei Tan ◽  
Zhao-Yang Yin
Keyword(s):  
Differential Equations ◽  
Wave Equations ◽  
Rogue Wave ◽  
Nonlinear Partial Differential Equations ◽  
Rogue Waves ◽  
Homoclinic Solutions ◽  
Nonlinear Wave Equations ◽  
Bilinear Method ◽  
Wave Solutions ◽  
Rogue Wave Solutions

Abstract The parameter limit method on the basis of Hirota’s bilinear method is proposed to construct the rogue wave solutions for nonlinear partial differential equations (NLPDEs). Some real and complex differential equations are used as concrete examples to illustrate the effectiveness and correctness of the described method. The rogue waves and homoclinic solutions of different structures are obtained and simulated by three-dimensional graphics, respectively. More importantly, we find that rogue wave solutions and homoclinic solutions appear in pairs. That is to say, for some NLPDEs, if there is a homoclinic solution, then there must be a rogue wave solution. The twin phenomenon of rogue wave solutions and homoclinic solutions of a class of NLPDEs is discussed.

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.

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