The new extended rational SGEEM for construction of optical solitons to the (2+1)–dimensional Kundu–Mukherjee–Naskar model

Abstract

This work proposes the new extended rational sinh-Gordon equation expansion technique (SGEEM). The computational approach is formulated based on the well-known sinh-Gordon equation. The proposed technique generalizes the sine-Gordon/sinh-Gordon expansion methods in a rational format. The efficiency of the suggested technique is tested on the (2+1)imensional Kunduukherjeeaskar (KMN) model. Various of optical soliton solutions have been obtained using this new method. The conditions which guarantee the existence of valid solitons are given.

Approximate Solutions for Dark and Singular Optical Solitons of Chen-Lee-Liu Model by Adomian-based Methods

“…Nevertheless, with regards to the CLL equation, very few computational techniques are available to numerically treat the model via the application of the standard Adomian's method and its modifications with particular types of soliton solutions [24][25][26][27][28][29]. Other similar numerical-based considerations to treat both the integer and non-integer order evolution equations and other broader forms of differential equations models are available in [30][31][32][33][34][35][36][37][38][39][40] and the references therein.…”

Traveling wave solutions for the generalized (2+1)-dimensional Kundu-Mukherjee-Naskar equation

“…(1). With the aid of extended rational sinh-Gordon equation expansion method [19], Sulaiman obtained the trigonometric functions solutions of Eq. ( 1).…”

A variety of exact solutions for fractional (2+1)-dimensional Heisenberg ferromagnetic spin chain in the semi classical limit

“…A large variety of these equations are utilized to describe important phenomena in different scientifi field like, plasma physics [1,2], condensed matter physics [3], convective fluid [5], optical fiber [6,7], solid state physics [8,9], hydrodynamic [10], water waves [11] and many other branches of engineering [12][13][14]. In past years, to fin the exact solutions of NLSEs many powerful technique have been developed such as, the inverse scattering transformation [15], the homotopy perturbation method [16,17], the Darboux transformation method [18,19], the Sine-Gordon expansion method [20], Bernoulli sub-equation method [21], the modifie auxiliary equation mapping method [22,23], the Riccati equation mapping method [4], the extended sinh-Gordon equation expansion method [24],the modify extended direct algebraic method [25].…”