Langrangian formulation and solitary wave solutions of a generalized Zakharov-Kuznetsov equation with dual power-law nonlinearity in physical sciences and engineering

In this research work, we investigated the higher-order nonlinear Schrödinger equation (NLSE) with fourth-order dispersion, self-steepening, nonlinearity, nonlinear dispersive terms and cubic-quintic terms which is described as the propagation of ultra-short pulses in fiber optics. We apply the modification form of extended auxiliary equation mapping method to find the new exact and solitary wave solutions of higher-order NLSE. As a result, new solutions are obtained in the form of solitons, kink–anti-kink type solitons, bright–dark solitons, traveling wave, trigonometric functions, elliptic functions and periodic solitary wave solutions. These new different types of solutions show the power and fruitfulness of this new method and also show two- and three-dimensional graphically with the help of computer software Mathematica. These new solutions have many applications in the field of physics and other branches of physical sciences. We can also solve other higher-order nonlinear partial differential equations (NPDEs) involved in mathematical physics and other various branches of physical sciences with this new technique.

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Dynamics of Different Nonlinearities to the Perturbed Nonlinear Schrödinger Equation via Solitary Wave Solutions with Numerical Simulation

Fractal and Fractional ◽

10.3390/fractalfract5040213 ◽

2021 ◽

Vol 5 (4) ◽

pp. 213

Author(s):

Asim Zafar ◽

Muhammad Raheel ◽

Muhammad Qasim Zafar ◽

Kottakkaran Sooppy Nisar ◽

Mohamed S. Osman ◽

...

Keyword(s):

Numerical Simulation ◽

Solitary Wave ◽

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Power Law ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Solitary Wave Solutions ◽

Nonlinear Schrödinger ◽

Wave Solutions

This paper investigates the solitary wave solutions for the perturbed nonlinear Schrödinger equation with six different nonlinearities with the essence of the generalized classical derivative, which is known as the beta derivative. The aforementioned nonlinearities are known as the Kerr law, power, dual power law, triple power law, quadratic–cubic law and anti-cubic law. The dark, bright, singular and combinations of these solutions are retrieved using an efficient, simple integration scheme. These solutions suggest that this method is more simple, straightforward and reliable compared to existing methods in the literature. The novelty of this paper is that the perturbed nonlinear Schrödinger equation is investigated in different nonlinear media using a novel derivative operator. Furthermore, the numerical simulation for certain solutions is also presented.

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Solitary wave solutions of the Vakhnenko–Parkes equation

Nonlinear Analysis Modelling and Control ◽

10.15388/na.17.1.14078 ◽

2012 ◽

Vol 17 (1) ◽

pp. 60-66 ◽

Cited By ~ 7

Author(s):

Fayequa Majid ◽

Houria Triki ◽

Tasawar Hayat ◽

Omar M. Aldossary ◽

Anjan Biswas

Keyword(s):

Solitary Wave ◽

Solitary Waves ◽

Power Law ◽

Solitary Wave Solutions ◽

Ansatz Method ◽

Wave Solutions

In this paper, two solitary wave solutions are obtained for the Vakhnenko–Parkes equation with power law nonlinearity by the ansatz method. Both topological as well as non-topological solitary wave solutions are obtained. The parameter regimes, for the existence of solitary waves, are identified during the derivation of the solution.

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New Extension for Sub Equation Method and its Application to the Time-fractional Burgers Equation by using of Fractional Derivative

TEMA (São Carlos) ◽

10.5540/tema.2017.018.02.0225 ◽

2017 ◽

Vol 18 (2) ◽

pp. 0225

Author(s):

Ahmad Neirameh

Keyword(s):

Solitary Wave ◽

Fractional Derivative ◽

Power Law ◽

Fractional Differential Equations ◽

Burgers Equation ◽

Equation Method ◽

Solitary Wave Solutions ◽

Fractional Complex Transform ◽

Wave Solutions ◽

Fractional Differential

In this paper, we use the new fractional complex transform and the sub equation method to study the nonlinear fractional differential equations and find the exact solutions. These solitary wave solutions demonstrate the fact that solutions to the perturbed nonlinear Schrodinger equation with power law nonlinearity model can exhibit a variety of behaviors.

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