White Noise Functional Solutions Research Articles

Hypercomplex Systems and Non-Gaussian Stochastic Solutions with Some Numerical Simulation of χ-Wick-Type (2 + 1)-D C-KdV Equations

In this article, we discuss the (2 + 1)-D coupled Korteweg–De Vries (KdV) equations whose coefficients are variables, and stochastic (2 + 1)-D C-KdV (C-KdV) equations with the χ-Wick-type product. White noise functional solutions (WNFS) are presented with the homogeneous equilibrium principle, Hermite transform (HT), and technicality via the F-expansion procedure. By means of the direct connection between the theory of hypercomplex systems (HCS) and white noise analysis (WNA), we establish non-Gaussian white noise (NGWN) by studying stochastic partial differential equations (PDEs) with NG-parameters. So, by using the F-expansion method we present multiples of exact and stochastic families from variable coefficients of travelling wave and stochastic NG-functional solutions of (2 + 1)-D C-KdV equations. These solutions are Jacobi elliptic functions (JEF), trigonometric, and hyperbolic forms, respectively.

White Noise Functional Solutions for Wick-Type Stochastic Fractional Mixed KdV-mKdV Equation Using Extended G ′ / G -Expansion Method

In this paper, white noise functional solutions of Wick-type stochastic fractional mixed KdV-mKdV equations have been obtained by using the extended G ′ / G -expansion method and the Hermite transform. Firstly, the Hermite transform is used to transform Wick-type stochastic fractional mixed KdV-mKdV equations into deterministic fractional mixed KdV-mKdV equations. Secondly, the exact traveling wave solutions of deterministic fractional mixed KdV-mKdV equations are constructed by applying the extended G ′ / G -expansion method. Finally, a series of white noise functional solutions are obtained by the inverse Hermite transform.

On exact special solutions for the stochastic regularized long wave-Burgers equation

In this paper, we will analyze the Regularized Long Wave-Burgers equation with conformable derivative (cd). Some white noise functional solutions for this equation are obtained by using white noise analysis, Hermite transforms, and the modified sub-equation method. These solutions include exact stochastic trigonometric functions, hyperbolic functions solutions and wave solutions.This study emphasizes that the modified fractional sub-equation method is sufficient to solve the stochastic nonlinear equations in mathematical physics.

Fractional white noise functional soliton solutions of a wick-type stochastic fractional NLSE

The wick-type stochastic fractional nonlinear Schrödinger equation is considered, and some analytical white noise functional solutions are found by the fractional F-expansion method with the Hermite transformation. The chirped and chirp-free fractional bright and dark soliton solutions with the Brownian motion function are constructed.

On exact solutions for the stochastic time fractional Gardner equation

In this work, the stochastic time fractional Gardner equation is analysed. Some white noise functional solutions for this equation are obtained by using white noise analysis, Hermite transforms and the modified fractional sub-equation method. These solutions include exact stochastic trigonometric functions, hyperbolic functions solutions and wave solutions.

The deterministic and stochastic solutions of the Schrodinger equation with time conformable derivative in birefrigent fibers

<abstract> <p>In this manuscript, the deterministic and stochastic nonlinear Schrödinger equation with time conformable derivative is analysed in birefrigent fibers. Hermite transforms, white noise analysis and the modified fractional sub-equation method are used to obtain white noise functional solutions for this equation. These solutions consists of exact stochastic hyperbolic functions, trigonometric functions and wave solutions.</p> </abstract>

Exact Solutions for a Class of Wick-Type Stochastic (3+1)-Dimensional Modified Benjamin–Bona–Mahony Equations

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.

NEW TRAVELLING WAVE SOLUTIONS FOR STOCHASTIC CUBIC NON LINEAR KLEIN-GORDON EQUATION

This paper is devoted to give white noise functional solutions for stochastic cubic nonlinear Klein-Gordon equation. Abundant exact travelling wave solutions for Wick-type generalized stochastic Klein-Gordon equation are obtained. By using white noise analysis, Hermite transform, modified Riccati equation and modified tanh-coth method many exact travelling wave solutions are given. Detailed computations and implemented examples for the investi- gated model are explicitly provided.

Exact Travelling Wave Solutions for Stochastic Fractional Hirota-Satsuma Coupled KdV Equations

A modied fractional sub-equation method is used for constructing exact travelling wave solutions of nonlinear stochastic fractional partial dierential equations. The main idea of this method is to take full advantage of the fractional Riccati equation, which has many exact solutions. Moreover, white noise functional solutions are obtained for the Wick-type stochastic fractional Hirota-Satsuma coupled KdV equations via Hermite transform and white noise analysis. These solutions include stochastic exponential decay, soliton, and periodic wave solutions.

Exact solution of the Wick-type stochastic fractional coupled KdV equations

Fractional differential equations are widely used to model many physical phenomena in science and engineering. This paper investigates the exact solutions of Wick-type stochastic fractional variable coefficients coupled KdV equations. By implementing fractional sub-equation method based on the Kudryashov technique, new families of exact travelling wave solutions are obtained. Moreover, the obtained white noise functional solutions can be expressed as exponential type. In particular, the stochastic fractional model is reduced into a deterministic fractional one by using the Hermite transform. The results reveal that the proposed technique is very effective and simple for obtaining exact solutions of stochastic fractional partial differential equations.

Analytical Approach to Exact Solutions for the Wick-Type Stochastic Space-Time Fractional KdV Equation

This study is devoted to giving an analytical approach to exact solutions for the Wick-type stochastic spacetime fractional KdV equation. By means of Hermite transform, white noise theory, and the fractional Riccati equation method, we derive white noise functional solutions for the Wick-type stochastic space-time fractional KdV equations. Exact traveling wave solutions for the variable coefficients space-time fractional KdV equations are given by using the fractional Riccati equation method. The obtained results include soliton-like, periodic, and rational solutions.

Exact Solutions for Stochastic Fractional Zakharov-Kuznetsov Equations

The main aim of this paper is to give exact solutions for the space-time-fractional Zakharov-Kuznetsov equation modified with variable coefficients. Our proposed technique is based on employing white noise analysis, Hermite transform, the homogeneous balance principle, and a modified tanh-coth method. Some white noise functional solutions for Wick-type stochastic space-time-fractional Zakharov-Kuznetsov equations with variable coefficients are established. Detailed computations and an implemented example are explicitly provided.

The fractional coupled KdV equations: Exact solutions and white noise functional approach

Variable coefficients and Wick-type stochastic fractional coupled KdV equations are investigated. By using the modified fractional sub-equation method, Hermite transform, and white noise theory the exact travelling wave solutions and white noise functional solutions are obtained, including the generalized exponential, hyperbolic, and trigonometric types.

White noise functional solutions for system of stochastic fractional coupled KdV equations

White noise functional solutions for system of stochastic fractional coupled KdV equations

Hyperbolic white noise functional solutions of Wick-type stochastic compound KdV–Burgers equations

Variable coefficient and Wick-type stochastic compound KdV–Burgers equations are investigated. By using white noise analysis, Hermite transform and the hyperbolic function method, we obtain a number of Wick versions of hyperbolic white noise functional solutions and hyperbolic function solutions for Wick-type stochastic and variable coefficient compound KdV–Burgers equations, respectively.

White noise functional solutions of Wick-type stochastic generalized Hirota–Satsuma coupled KdV equations

Generalized Hirota–Satsuma coupled KdV equations with variable coefficients and Wick-type stochastic generalized Hirota–Satsuma coupled KdV equations are investigated. White noise functional solutions are shown by Hermite transform, homogeneous balance principle and F-expansion method.