Bright, dark and W-shaped solitons with extended nonlinear Schrödinger's equation for odd and even higher-order terms

New exact optical soliton solutions for nonlinear Schrödinger equation with second-order spatio-temporal dispersion involving M-derivative

“…The exact solution of this equation is important in optics, optical communication areas, electromagnetism, plasma and fluids. [1][2][3][4][5][6][7][8][9][10][11][12][13] During the last decades, a wide variety of analytic methods have been proposed to solve partial differential equation arising in various physical aspects of applied sciences. [14][15][16][17][18][19] In this paper, we consider the generalized exponential rational function method.…”

Optical solitons to the fractional Schrödinger-Hirota equation

“…Optical solitons are restrained electromagnetic waves that stretch in nonlinear dispersive media and allow the intensity to remain unchanged due to the balance between dispersion and nonlinearity effects [4]. Various analytical approaches for securing optical solitons and other solutions to different kind of NLSEs have been reported to the literature such as the the sine-Gordon expansion method [5][6][7], the first integral method [8,9], the improved Bernoulli sub-equation function method [10,11], the trial solution method [12,13], the new auxiliary equation method [14], the extended simple equation method [15], the solitary wave ansatz method [16], the functional variable method [17], the sub-equation method [18][19][20] and several others [21][22][23][24][25][26][27][28][29][30][31][32][33].…”

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

“…This area has drawn the attention of many scientists for more than two decades. Different computational methods have been used to reveal solutions of various type of NLEEs such as the modified exp(−Ψ(η))-expansion function method [7][8][9], the first integral method [10,11], the improved Bernoulli sub-equation function method [12,13], the trial solution method [14,15], the new auxiliary equation method [16], the extended simple equation method [17], the solitary wave ansatz method [18], the functional variable method [19] and several others [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39].…”