Resonance nonlinear wave phenomena with obliqueness and fractional time evolution via the novel auxiliary ordinary differential equation method

Abstract

In this article, the oblique resonance wave phenomena are investigated by considering nonlinear coupled evolution equations with fractional time evolution. In order to investigate such physical phenomena arising in many branches of physics, the time fractional coupled (2 + 1)-dimensional nonlinear Schrodinger and long-short wave resonance interaction evolution equations are considered. The analytical solutions of considered equations are achieved by implementing the proposed auxiliary ordinary differential equation method along with the properties of Khali's fractional derivatives. The obtained outcomes may be useful for better understanding the basic properties of internal oblique propagating wave dynamics in many branches of science and engineering.

Dynamical plane wave solutions for the Heisenberg model of ferromagnetic spin chains with beta derivative evolution and obliqueness

“…According to the homogeneous balance principle and AODEM (see details in Ref. [39] ), the oblique solutions of Eq. (6) can be expressed as a polynomial in : where, are constants with .…”

“…(10) offers a variety of solutions by applying to the actual parametric values p , q and r as set out in Ref. [39] . With the help of Eq.…”

“…To overcome such difficulties, researchers have concentrated their efforts on fractional derivatives (FDs), such as conformable, Caputo, Riemann-Liouville derivatives, etc., in lieu of classical derivatives. Such FDs have been introduced in many mathematical physics equations [20] , [31] , [32] , [34] , [35] , [36] , [37] , [38] , [39] to understand the complex physical issues in the physical system. Very recently, the newly included FD, so called the Beta derivative (BD), has been proposed by Atangana et al [37] , which fulfills all the fundamental features of calculus and overcomes some limitations of the aforementioned FDs.…”

“…Thus, this work explores the bifurcation analysis of plane waves by forming PDS from the considered equation. In addition, some more new analytical forms of OPWSs are determined by employing two useful techniques, namely, the auxiliary ordinary differential equation method (AODEM) [32] , [39] and the extended simplest equation method (ESEM) [33] . The effect of BD parameter and obliqueness on several types of wave structures, along with the phase portrait diagrams are examined.…”