White noise theory and general improved Kudryashov method for stochastic nonlinear evolution equations with conformable derivatives

Advances in Difference Equations

article

Hyder, Abd-Allah¹ 

[1] Department of Mathematics, College of Science, King Khalid University;Department of Engineering Mathematics and Physics, Faculty of Engineering, Al-Azhar University

关键词: Kudryashov method;    Combined KdV–mKdV equation;    Nonlinear evolution equations;    Conformable derivatives;    Exact solutions;    Stochastic;   

DOI  :  10.1186/s13662-020-02698-7

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

The aim of this work is to investigate the Wick-type stochastic nonlinear evolution equations with conformable derivatives. The general Kudryashov method is improved by a new auxiliary equation. So, a new technique, which we call “the general improved Kudryashov method (GIKM)”, is introduced to produce exact solutions for the nonlinear evolution equations with conformable derivatives. By means of GIKM, white noise theory, Hermite transform, and computerized symbolic computation, a novel technique is presented to solve the Wick-type stochastic nonlinear evolution equations with conformable derivatives. This technique is applied to construct exact traveling wave solutions for Wick-type stochastic combined KdV–mKdV equation with conformable derivatives. Moreover, numerical simulations with 3D profiles are shown for the obtained results.

【 授权许可】

CC BY