Travelling wave solutions of generalized coupled Zakharov-Kuznetsov and dispersive long wave equations
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In this paper, the authors constructed different form of new exact solutions of generalized coupled Zakharov-Kuznetsov and dispersive long wave equations by utilizing the modified extended direct algebraic method.Abstract:
In this manuscript, we constructed different form of new exact solutions of generalized coupled Zakharov–Kuznetsov and dispersive long wave equations by utilizing the modified extended direct algebraic method. New exact traveling wave solutions for both equations are obtained in the form of soliton, periodic, bright, and dark solitary wave solutions. There are many applications of the present traveling wave solutions in physics and furthermore, a wide class of coupled nonlinear evolution equations can be solved by this method.read more
Citations
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Applications of extended simple equation method on unstable nonlinear Schrödinger equations
TL;DR: In this article, the extended form of simple equation method (SEM) is employed to construct exact travelling wave solutions of unstable nonlinear schroodinger equation and modify unstable non linear schrodinger equation.
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Two-dimensional interaction of a shear flow with a free surface in a stratified fluid and its solitary-wave solutions via mathematical methods
Aly R. Seadawy,Aly R. Seadawy +1 more
TL;DR: In this article, the authors presented the problem formulations of models for internal solitary waves in a stratified shear flow with a free surface and derived the coefficients of the nonlinear higher-order extended KdV equation in terms of integrals of the modal function for the linear long-wave theory.
Journal ArticleDOI
Exact bright-dark solitary wave solutions of the higher-order cubic-quintic nonlinear Schrödinger equation and its stability
TL;DR: In this paper, an extended form of simple equation method is proposed to construct exact soliton and solitary wave solutions of higher-order nonlinear Schrodinger equation with fourth-order dispersion and cubic-quintic nonlinearity.
Journal ArticleDOI
Travelling wave solutions of Drinfel’d–Sokolov–Wilson, Whitham–Broer–Kaup and (2+1)-dimensional Broer–Kaup–Kupershmit equations and their applications
TL;DR: In this paper, some exact travelling wave solutions are constructed in different form of coupled partial differential equations having terms of odd and even order partial derivative, by applying modified extended direct algebraic method.
Journal ArticleDOI
Stability analysis of new exact traveling-wave solutions of new coupled KdV and new coupled Zakharov-Kuznetsov systems
TL;DR: In this article, the modified extended direct algebraic method on new coupled systems, which have many important applications in mathematical physics, is further extended to new coupled KdV and Zakharov-Kuznetsov (ZK) systems.
References
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Book
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M. A. Ablowitz,Peter A. Clarkson +1 more
TL;DR: In this article, the authors bring together several aspects of soliton theory currently only available in research papers, including inverse scattering in multi-dimensions, integrable nonlinear evolution equations in multidimensional space, and the ∂ method.
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D. J. de Korteweg,G. de Vries +1 more
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Exact Solution of the Korteweg-de Vries Equation for Multiple Collisions of Solitons
TL;DR: An exact solution for the Korteweg-de Vries equation for the case of multiple collisions of $N$ solitons with different amplitudes was obtained in this paper, which is the only known exact solution.
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Exact solutions for a compound KdV-Burgers equation
TL;DR: In this article, the exact solutions of a compound KdV-Burgers equation are obtained by using a homogeneous balance method, which can be used to solve a number of important cases of the equation.
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