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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. [ABSTRACT FROM AUTHOR]

Wick-type two-dimensional stochastic Zakharov-Kuznetsov is researched. By means of Hermite transformation, white noise theory, extended homogeneous balance principle and a new auxili-ary equation, we uniformly construct a general formal solution for the Wick-type two-dimensional stochastic Zakharov-Kuznetsov with variable coefficients. With the help of the mapping relation constructed between the general formal solution of the Wick-type twodimensional stochastic Zakharov-Kuznetsov and the solutions of the auxiliary equation, various types of exact solutions of the Wick-type two-dimensional stochastic Zakharov-Kuznetsov are derived. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the Wick-type stochastic (3+1)-dimensional modified Benjamin–Bona–Mahony (BBM) equations. We present a generalised version of the modified tanh–coth method. Using the generalised, modified tanh–coth method, white noise theory, and Hermite transform, we produce a new set of exact travelling wave solutions for the (3+1)-dimensional modified BBM equations. This set includes solutions of exponential, hyperbolic, and trigonometric types. With the help of inverse Hermite transform, we obtained stochastic travelling wave solutions for the Wick-type stochastic (3+1)-dimensional modified BBM equations. Eventually, by application example, we show how the stochastic solutions can be given as white noise functional solutions. [ABSTRACT FROM AUTHOR]

A modified fractional sub-equation method is applied to Wick-type stochastic fractional two-dimensional (2D) KdV equations. With the help of a Hermit transform, we obtain a new set of exact stochastic solutions to Wick-type stochastic fractional 2D KdV equations in the white noise space. These solutions include exponential decay wave solutions, soliton wave solutions, and periodic wave solutions. Two examples are explicitly given to illustrate our approach. [ABSTRACT FROM AUTHOR]