scholarly journals A novel analytical algorithm for generalized fifth-order time-fractional nonlinear evolution equations with conformable time derivative arising in shallow water waves

2021 ◽  
Author(s):  
Omar Abu Arqub ◽  
Mohammed Al-Smadi ◽  
Hassan Almusawa ◽  
Dumitru Baleanu ◽  
Tasawar Hayat ◽  
...  
Keyword(s):  
Shallow Water ◽  
Water Waves ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Time Derivative ◽  
Nonlinear Evolution Equations ◽  
Shallow Water Waves ◽  
Analytical Algorithm ◽  
Fifth Order

scholarly journals Comment on “Two-dimensional third-and fifth-order nonlinear evolution equations for shallow water waves with surface tension” [Nonlinear Dyn,  doi:10.1007/s11071-017-3938-7]

2021 ◽  
Author(s):  
Piotr Rozmej ◽  
Anna Karczewska
Keyword(s):  
Surface Tension ◽  
Shallow Water ◽  
Water Waves ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Evolution Equations ◽  
Two Dimensional ◽  
Shallow Water Waves ◽  
Small Parameters ◽  
Fifth Order

AbstractThe authors of the paper “Two-dimensional third-and fifth-order nonlinear evolution equations for shallow water waves with surface tension” Fokou et al. (Nonlinear Dyn 91:1177–1189, 2018) claim that they derived the equation which generalizes the KdV equation to two space dimensions both in first and second order in small parameters. Moreover, they claim to obtain soliton solution to the derived first-order (2+1)-dimensional equation. The equation has been obtained by applying the perturbation method Burde (J Phys A: Math Theor 46:075501, 2013) for small parameters of the same order. The results, if correct, would be significant. In this comment, it is shown that the derivation presented in Fokou et al. (Nonlinear Dyn 91:1177–1189, 2018) is inconsistent because it violates fundamental properties of the velocity potential. Therefore, the results, particularly the new evolution equation and the dynamics that it describes, bear no relation to the problem under consideration.

scholarly journals Stability Analysis for Travelling Wave Solutions of the Olver and Fifth-Order KdV Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
A. R. Seadawy ◽  
W. Amer ◽  
A. Sayed
Keyword(s):  
Water Waves ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Travelling Wave ◽  
Nonlinear Evolution Equations ◽  
Shallow Water Waves ◽  
Kdv Equations ◽  
Wave Solutions ◽  
All Solutions ◽  
Fifth Order

The Olver equation is governing a unidirectional model for describing long and small amplitude waves in shallow water waves. The solitary wave solutions of the Olver and fifth-order KdV equations can be obtained by using extended tanh and sech-tanh methods. The present results are describing the generation and evolution of such waves, their interactions, and their stability. Moreover, the methods can be applied to a wide class of nonlinear evolution equations. All solutions are exact and stable and have applications in physics.

scholarly journals Analytical Solutions for Nonlinear Dispersive Physical Model

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Wen-Xiu Ma ◽  
Mohamed R. Ali ◽  
R. Sadat
Keyword(s):  
Water Waves ◽  
Nuclear Physics ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Travelling Wave ◽  
Lie Symmetries ◽  
Nonlinear Evolution Equations ◽  
Travelling Wave Solutions ◽  
Shallow Water Waves ◽  
Integrating Factor

Nonlinear evolution equations widely describe phenomena in various fields of science, such as plasma, nuclear physics, chemical reactions, optics, shallow water waves, fluid dynamics, signal processing, and image processing. In the present work, the derivation and analysis of Lie symmetries are presented for the time-fractional Benjamin–Bona–Mahony equation (FBBM) with the Riemann–Liouville derivatives. The time FBBM equation is reduced to a nonlinear fractional ordinary differential equation (NLFODE) using its Lie symmetries. These symmetries are derivations using the prolongation theorem. Applying the subequation method, we then use the integrating factor property to solve the NLFODE to obtain a few travelling wave solutions to the time FBBM.

Analytical wave solution for the generalized nonlinear seventh-order KdV dynamical equations arising in shallow water waves

2020 ◽  
Vol 34 (26) ◽  
pp. 2050279
Author(s):  
Noufe H. Aljahdaly ◽  
Aly R. Seadawy ◽  
Wafaa A. Albarakati
Keyword(s):  
Water Waves ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Kdv Equation ◽  
Algebraic Method ◽  
Analytic Solutions ◽  
Nonlinear Evolution Equations ◽  
Shallow Water Waves ◽  
Dynamical Equations ◽  
Seventh Order

Finding solitary wave solutions of Nonlinear evolution equations are of great interest. The direct algebraic method was used here to find the analytic solutions to the generalized seventh-order KdV equation which plays an important role in engineering and mathematical physics.

scholarly journals A Novel Analytical Technique to Obtain Kink Solutions for Higher Order Nonlinear Fractional Evolution Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Qazi Mahmood Ul Hassan ◽  
Jamshad Ahmad ◽  
Muhammad Shakeel
Keyword(s):  
Differential Equation ◽  
Exact Solutions ◽  
Fractional Derivatives ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Evolution Equations ◽  
Fractional Evolution Equations ◽  
Analytical Technique ◽  
Fractional Complex Transform ◽  
Fifth Order

We use the fractional derivatives in Caputo’s sense to construct exact solutions to fractional fifth order nonlinear evolution equations. A generalized fractional complex transform is appropriately used to convert this equation to ordinary differential equation which subsequently resulted in a number of exact solutions.

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