The development of the deterministic nonlinear PDEs in particle physics to stochastic case

In this work, we have suggested a neat method of obtaining the fractional diffusion equation for an anomalous anisotropic diffusion process using fractal brush structure as a background medium. For the sake of completeness, we intend to present an analytical solution in the case of the Dirichlet boundary condition. Finally, some notes and remarks are represented to show the vital role of a physical or biological system that exhibits a multiple trapping process.

Section: Mathematical Solutionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Fractional anisotropic diffusion equation in cylindrical brush model

Sharaf

El-Shewy

Zahran

2020

“…In recent years, many researchers have tried to find exact solutions of the nonlinear partial differential equations (NPDEs), which play an important role in nonlinear science and engineering, for instance, fluid mechanics, meteorology, plasma physics, solid state physics, heat flow and chemical engineering [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. As a result, many new methods have been successfully investigated and proposed like tanh-sech method [15], homogeneous balance method [16], exp-function method [17], Riccati-Bernoulli (RB) sub-ODE method [18][19][20], sine-cosine method [21], He's variational method [22], homotopy perturbation method [23], trigonometric function series method [24], (G /G)−expansion method [25], Jacobi elliptic function method [26] and trial solution method [27].…”

Section: Introductionmentioning

confidence: 99%

Disturbance solutions for the long–short-wave interaction system using bi-random Riccati–Bernoulli sub-ODE method

Alharbi

Abdelrahman

Sohaly

et al. 2020

Self Cite

This article applied the Riccati-Bernoulli (RB) sub-ODE method in order to get new exact solutions for the long-short-wave interaction (LS) equations. Namely, we obtain deterministic and random solutions, since we consider the proposed method in deterministic and random cases. The RB sub-ODE technique gives the travelling wave solutions in forms of hyperbolic, trigonometric and rational functions. It is shown that the proposed method gives a robust mathematical tool for solving nonlinear wave equations in applied science. Furthermore, some bi-random variables and some random distributions are used in random case corresponding to the LS system. The stability for the obtained solutions in random case is considered. In addition, there is a display of several numerical simulations, which helps to understand the physical phenomena of these soliton wave solutions. ARTICLE HISTORY

“…Recently, there is a huge development in analytical methods for getting solutions for NPDEs, see [24][25][26][27][28][29][30][31][32][33][34][35][36] and references therein. So, the aim of this work is to use one of these methods to introduce new solution forms applicable for auroral zone observations.…”

Section: Introductionmentioning

confidence: 99%

Super electron acoustic propagations in critical plasma density

Abdelwahed

2020

The propagation of some new electrostatic cnoidal, super-solitons, super-periodic and shocklike waves in Earth magneto-tail electron acoustic (EA) plasma at critical density has been investigated via MKP equation. These MKP solutions are obtained by the method of expansion Jacobian elliptic function (EMJEF). Numerous of the given solutions are significant on the observations of broadband electrostatic nonlinear noise forms in layers of magneto-tail.