Modified Kudrayshov Method to Solve Generalized Kuramoto&amp;ndash;Sivashinsky Equation

Kılıçman, Adem; Silambarasan, Rathinavel

doi:10.20944/preprints201808.0372.v2

2018

DOI: 10.20944/preprints201808.0372.v2

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Modified Kudrayshov Method to Solve Generalized Kuramoto–Sivashinsky Equation

Adem Kılıçman¹,

Rathinavel Silambarasan²

Abstract: The generalized Kuramoto–Sivashinsky equation is investigated using the modified Kudrayshov method for the exact analytical solution. The modified Kudrayshov method converts the nonlinear partial differential equation to algebraic equations, as a result of various steps, which on solving the so obtained equation systems yields the analytical solution. By this way various exact solutions including complex structures are found and drawn their behaviour in complex plane by Maple to compare the uniquenes… Show more

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Solving Schrödinger–Hirota Equation in a Stochastic Environment and Utilizing Generalized Derivatives of the Conformable Type

et al. 2021

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This work is devoted to providing new kinds of deterministic and stochastic solutions of one of the famous nonlinear equations that depends on time, called the Schrödinger–Hirota equation. A new and straightforward methodology is offered to extract exact wave solutions of the stochastic nonlinear evolution equations (NEEs) with generalized differential conformable operators (GDCOs). This methodology combines the features of GDCOs, some instruments of white noise analysis, and the generalized Kudryashov scheme. To demonstrate the usefulness and validity of our methodology, we applied it to extract diversified exact wave solutions of the Schrödinger–Hirota equation, particularly in a Wick-type stochastic space and with GDCOs. These wave solutions can be turned into soliton and periodic wave solutions that play a main role in numerous fields of nonlinear physical sciences. Moreover, three-dimensional, contour, and two-dimensional graphical visualizations of some of the extracted solutions are exhibited with some elected functions and parameters. According to the results, our new approach demonstrates the impact of random and conformable factors on the solutions of the Schrödinger–Hirota equation. These findings can be applied to build new models in plasma physics, condensed matter physics, industrial studies, and optical fibers. Furthermore, to reinforce the importance of the acquired solutions, comparative aspects connected to some former works are presented for these types of solutions.

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Solving Schrödinger–Hirota Equation in a Stochastic Environment and Utilizing Generalized Derivatives of the Conformable Type

et al. 2021

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Modified Kudrayshov Method to Solve Generalized Kuramoto–Sivashinsky Equation

Cited by 1 publication

References 18 publications

Solving Schrödinger–Hirota Equation in a Stochastic Environment and Utilizing Generalized Derivatives of the Conformable Type

Solving Schrödinger–Hirota Equation in a Stochastic Environment and Utilizing Generalized Derivatives of the Conformable Type

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