New travelling wave solutions to (2+1)-Heisenberg ferromagnetic spin chain equation using Atangana’s conformable derivative

Abstract

In this study, some new optical soliton solutions are obtained with generalized Riccati equation mapping method for space time conformable (2+1) dimensional Heisenberg ferromagnetic spin chain equation by using Atangana’s conformable derivative. We construct bright and dark solitons, combined bright-dark solitons, periodic wave solutions for this equation. 3D and 2D graphs of few obtained solutions are plotted to show some interesting physical features as these new results might be helpful in the study of nonlinear ferromagnetic materials and optical fibers. The procured results show that this is very robust method to originate abundant solutions for various fractional differential equations. All the results are verified by Maple program.

A new implementation of a novel analytical method for finding the analytical solutions of the (2+1)-dimensional KP-BBM equation

“…There are several methods to solve and find the exact solutions to the evolution equations involving non-linearity. For example, the -expansion method [6] , [7] , [8] , [9] , the exp-function method [10] , the modified exp-function method [11] , [12] , the tanh–coth expansion method [13] , [14] , [15] , the improved method [16] , [17] , the -expansion method [18] , [19] , [20] , [21] , the simple equation method (SEM) [22] , [23] , the Lie symmetry approach [24] , [25] , the sine-Gordon method [26] , the modified Sardar sub-equation method [27] , [28] , the generalized Kudryashov method [29] , [30] , the Riccati-Bernoulli sub-ODE method [31] , [32] , the improved generalized Riccati mapping method [33] , the modified double sub-equation method [34] , the generalized exponential rational function (GERF) method [35] , [36] and there are many more. Beside these integer order PDEs there are lots of techniques for investigating fractional order PDEs such as [37] , [38] etc.…”

The solitary wave solutions of the stochastic Heisenberg ferromagnetic spin chain equation using two different analytical methods

“…It plays an important role in the modern magnetic theory, which describes nonlinear magnet dynamics and is used in optical fibers. Due to the importance of DHFE, many authors have attained the exact solution for this equation by using various methods, such as Hirota's bilinear method [13,14], Darboux transformation [15][16][17], sub-ODE method [18], sine-Gordon and modified exp-function expansion methods [19], auxiliary ordinary differential equation [20], Jacobi elliptic functions [21], F-expansion method combined with Jacobi elliptic functions [22], and generalized Riccati mapping method and improved auxiliary equation [23], while many authors have investigated the analytical solutions of fractional DHFE by using various methods, including exp (−ϕ(ς))-expansion and extended tanh function [24], new extended generalized Kudryashov [25], and generalized Riccati equation mapping methods [26].…”

Soliton and other solutions of the (2+1)-dimensional Date-Jimbo-Kashiwara-Miwa equation with conformable derivative

“…Also, very effective mathematical techniques have been developed and utilized for NLPDEs. Some of these techniques are the generalized Riccati equation mapping method [1,2] , the modified extended tanh expansion method combined with new Riccati solutions [3], the extended rational sine-cosine/sinh-cosh method [4,5],the modified extended tanh expansion method [6][7][8], the simplified bilinear method [9], the polynomial-function method [9,10], the Kudryashovexpansion method [9], the Riccati-Bernoulli sub-ODE technique [11,12], the Sardar-subequation method [13], the Jacobi elliptic function expansion method [14], the sine-Gordon expansion method [15], the sub-equation method [16,17], the q-homotopy analysis transform method [18], Hirotas bilinear structure [19], the Lie symmetry method [20], Haar wavelet method [21] and so on.…”