A multiple exp-function method for the three model equations of shallow water waves

2017 ◽  
Vol 89 (3) ◽  
pp. 2291-2297 ◽  
Author(s):  
Yakup Yildirim ◽  
Emrullah Yasar ◽  
Abdullahi Rashid Adem
Keyword(s):  
Shallow Water ◽  
Water Waves ◽  
Function Method ◽  
Shallow Water Waves ◽  
Model Equations

scholarly journals Shallow water waves in porous medium for coast protection

2017 ◽  
Vol 21 (suppl. 1) ◽  
pp. 145-151 ◽  
Author(s):  
Yan Wang ◽  
Yufeng Zhang ◽  
Wenjuan Rui
Keyword(s):  
Porous Medium ◽  
Shallow Water ◽  
Water Waves ◽  
Function Method ◽  
Travelling Wave ◽  
Basic Solution ◽  
Solution Properties ◽  
Shallow Water Waves ◽  
Fractional Complex Transform ◽  
Fractional Momentum

This paper extends the Hirota-Satsuma equation in continuum mechanics to its fractional partner in fractal porous media in shallow water for absorbing wave energy and preventing tsunami. Its derivation is briefly introduced using the fractional momentum law and He?s fractional derivative. The fractional complex transform is adopted to elucidate its basic solution properties, and a modification of the exp-function method is used to solve the equation. The paper concludes that the kinetic energy of the travelling wave tends to be vanished when the value of the fractional order is less than one.

scholarly journals Nonlinear self adjointness, conservation laws and exact solutions of ill-posed Boussinesq equation

Open Physics ◽  
2016 ◽  
Vol 14 (1) ◽  
pp. 37-43 ◽  
Author(s):  
Emrullah Yaşar ◽  
Sait San ◽  
Yeşim Sağlam Özkan
Keyword(s):  
Conservation Laws ◽  
Exact Solutions ◽  
Shallow Water ◽  
Water Waves ◽  
Function Method ◽  
Boussinesq Equation ◽  
Lie Point Symmetries ◽  
Shallow Water Waves ◽  
Non Linear ◽  
Ill Posed

AbstractIn this work, we consider the ill-posed Boussinesq equation which arises in shallow water waves and non-linear lattices. We prove that the ill-posed Boussinesq equation is nonlinearly self-adjoint. Using this property and Lie point symmetries, we construct conservation laws for the underlying equation. In addition, the generalized solitonary, periodic and compact-like solutions are constructed by the exp-function method.

scholarly journals Approximate Numerical solutions for the nonlinear dispersive shallow water waves as the Fornberg–Whitham model equations

2021 ◽  
Vol 22 ◽  
pp. 103907 ◽  
Author(s):  
Hijaz Ahmad ◽  
Aly R. Seadawy ◽  
Abdul Hamid Ganie ◽  
Saima Rashid ◽  
Tufail A. Khan ◽  
...  
Keyword(s):  
Shallow Water ◽  
Water Waves ◽  
Numerical Solutions ◽  
Shallow Water Waves ◽  
Model Equations
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