Novel solitary waves for fractional (2+1)-dimensional Heisenberg ferromagnetic model via new extendedgeneralized Kudryashov method

Abstract

This article introduces the fractional (2+1)-dimensional evolution model portraying the transmission of nonlinear spin dynamics in Heisenberg ferromagnetic spin chains with bilinear and anisotropic interactions in the semiclassical limit. Fractional derivatives stand out in modeling problems involving the concepts of non-locality and memory effect, that are not well explained by the integer-order calculus. New extended generalized Kudryashov method is employed to construct traveling wave solutions of governing equation. These solutions such as dark, singular solitons, solitary waves and singular solitary waves arise with constraint conditions and exhibit distinct physical significance. Since magnetic soliton has been classified as one of the fascinating groups of nonlinear excitations expressing spin dynamics in semiclassical continuum Heisenberg systems. 3D and 2D graphs for suitable parametric values are provided to interpret the dynamics of soliton profiles. Also, a comparative analysis is shown among Beta and Atangana-Baleanu fractional derivatives. Our results assert that this scheme is reliable and efficient gadget for extracting the soliton solutions of different nonlinear evolution equations appearing in mathematical sciences.

Integrability, Variational Principle, Bifurcation, and New Wave Solutions for the Ivancevic Option Pricing Model

“…where ± ϕ 1 are the real roots for the quartic polynomial (37). Hence, we obtain a new solution for equation ( 4) in the following formula: Integrating equation (36) along one of these orbits, we obtain…”

“…where ± φ 1,2 are the roots of the polynomial (37) with 0 < φ < φ 1 < φ 2 . Hence, equation ( 4) has a new solution in the following formula:…”

“…Researchers are therefore motivated to present new methods and refine existing approaches. Various significant and powerful methods have been introduced such as Darboux transformation [14], Weierstrass elliptic functions methods [15,16], Bäcklund transformation [17], Lie group [18][19][20][21], Hirota's method [22,23], bifurcation method [24][25][26][27][28][29][30][31][32][33], and for distinct method, as shown in e.g., [34][35][36][37][38][39][40][41][42]. e analytical and numerical solutions for various types of nonlinear partial differential equations were investigated using traditional Lie symmetry approaches; for instance as shown in [43].…”

New lump solutions to the nonlinear Schrödinger equation under the few-cycle pulse propagation property

“…Indeed, we concentrate our attention on the nonlinear Schrödinger equation that models the dynamic of waves in such materials. The arising solitons and other analytical solutions to different forms of Schrödinger models have been widely studied by the authors [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. The few-cycle pulse propagation in metamaterials specially is one of nonlinear Schrödinger applications and its solutions are helpful to understands more deeply the concerned materials.…”

Novel Analytical Approach for the Space-Time Fractional (2+1)-Dimensional Breaking Soliton Equation via Mathematical Methods

“…The plethora of attention has been received to determine the incipient and closed form exact solutions of FPDEs by many researchers. The potential symbolic computer programming implements have been utilized to investigate opportune solutions to NFPDEs, namely, first integral method [3][4][5], modified simple equation schemes [6,7], dirct agebric methods and auxiliary equation techniques [8][9][10], fractional equation scheme [11][12][13][14], (G /G) -expansion scheme [15][16][17], Lie-symmetry technique [18], Seadawy and Exp function methods [19][20][21][22], tanh-coth scheme [23], generalized Kudryashov scheme [24][25][26][27][28][29] and many more [30][31][32][33][34][35][36][37][38].…”