scholarly journals The new exact solitary wave solutions and stability analysis for the ( 2 + 1 ) $(2+1)$ -dimensional Zakharov–Kuznetsov equation

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Behzad Ghanbari ◽  
Abdullahi Yusuf ◽  
Mustafa Inc ◽  
Dumitru Baleanu
Keyword(s):  
Stability Analysis ◽  
Solitary Wave ◽  
Solitary Wave Solutions ◽  
Wave Solutions

scholarly journals New solitary wave solutions and stability analysis of the Benney-Luke and the Phi-4 equations in mathematical physics

2019 ◽  
Vol 4 (6) ◽  
pp. 1523-1539 ◽  
Author(s):  
Behzad Ghanbari ◽  
◽  
Mustafa Inc ◽  
Abdullahi Yusuf ◽  
Dumitru Baleanu ◽  
...  
Keyword(s):  
Stability Analysis ◽  
Solitary Wave ◽  
Mathematical Physics ◽  
Solitary Wave Solutions ◽  
Wave Solutions

Stability analysis and abundant closed-form wave solutions of the Date–Jimbo–Kashiwara–Miwa and combined sinh–cosh-Gordon equations arising in fluid mechanics

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Aly R. Seadawy ◽  
Asghar Ali
Keyword(s):  
Applied Sciences ◽  
Stability Analysis ◽  
Solitary Wave ◽  
Fluid Mechanics ◽  
Exact Solutions ◽  
Solitary Wave Solutions ◽  
Mathematical Methods ◽  
Special Values ◽  
Wave Solutions ◽  
Diverse Form

Abstract In this manuscript, several types of exact solutions including trigonometric, hyperbolic, exponential, and rational function are successfully constructed with the implementation of two modified mathematical methods, namely called extended simple equation and modified F-expansion methods on the (2 + 1)-dimensional Date–Jimbo–Kashiwara–Miwa and the combined sinh–cosh-Gordon equations. Diverse form of solitary wave solutions is achieved from exact solutions by passing the special values to the parameters. Some solution are plotted in the form of 3D and 2D by assigning the specific values to parameters under the constrain condition to the solutions. These approaches yield the new solutions that we think other researchers have missed in the field of nonlinear sciences. Hence the searched wave’s results are loyal to the researchers and also have imperious applications in applied sciences.

scholarly journals Bifurcation, Traveling Wave Solutions, and Stability Analysis of the Fractional Generalized Hirota–Satsuma Coupled KdV Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Zhao Li ◽  
Peng Li ◽  
Tianyong Han
Keyword(s):  
Stability Analysis ◽  
Solitary Wave ◽  
Traveling Wave ◽  
Bifurcation Theory ◽  
Traveling Wave Solutions ◽  
Phase Portraits ◽  
Solitary Wave Solutions ◽  
Kdv Equations ◽  
Wave Solutions ◽  
Coupled Kdv Equations

In this paper, the bifurcation, phase portraits, traveling wave solutions, and stability analysis of the fractional generalized Hirota–Satsuma coupled KdV equations are investigated by utilizing the bifurcation theory. Firstly, the fractional generalized Hirota–Satsuma coupled KdV equations are transformed into two-dimensional Hamiltonian system by traveling wave transformation and the bifurcation theory. Then, the traveling wave solutions of the fractional generalized Hirota–Satsuma coupled KdV equations corresponding to phase orbits are easily obtained by applying the method of planar dynamical systems; these solutions include not only the bell solitary wave solutions, kink solitary wave solutions, anti-kink solitary wave solutions, and periodic wave solutions but also Jacobian elliptic function solutions. Finally, the stability criteria of the generalized Hirota–Satsuma coupled KdV equations are given.

scholarly journals Construction of new solitary wave solutions of generalized Zakharov-Kuznetsov-Benjamin-Bona-Mahony and simplified modified form of Camassa-Holm equations

Open Physics ◽  
2018 ◽  
Vol 16 (1) ◽  
pp. 896-909 ◽  
Author(s):  
Dianchen Lu ◽  
Aly R. Seadawy ◽  
Mujahid Iqbal
Keyword(s):  
Solitary Wave ◽  
Nonlinear Partial Differential Equations ◽  
Research Work ◽  
Traveling Wave Solutions ◽  
Elliptic Functions ◽  
Mapping Method ◽  
New Method ◽  
Auxiliary Equation ◽  
Solitary Wave Solutions ◽  
Wave Solutions

AbstractIn this research work, for the first time we introduced and described the new method, which is modified extended auxiliary equation mapping method. We investigated the new exact traveling and families of solitary wave solutions of two well-known nonlinear evaluation equations, which are generalized Zakharov-Kuznetsov-Benjamin-Bona-Mahony and simplified modified forms of Camassa-Holm equations. We used a new technique and we successfully obtained the new families of solitary wave solutions. As a result, these new solutions are obtained in the form of elliptic functions, trigonometric functions, kink and antikink solitons, bright and dark solitons, periodic solitary wave and traveling wave solutions. These new solutions show the power and fruitfulness of this new method. We can solve other nonlinear partial differential equations with the use of this method.

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