Dynamics of the self-similar Kink and rational solitary waves in a dual power-law medium

Some optical solitons and modulation instability analysis of (3 + 1)-dimensional nonlinear Schrödinger and coupled nonlinear Helmholtz equations

“…In addition to these approaches, there are numerous other approaches that use an auxiliary equation to arrive at a solution. These methods are given in (Malfliet 1992;Fan 2000a, b;Elwakil et al 2002;Chen and Zhang 2004;Fu et al 2001;Shen and Pan 2003;Chen and Hong-Qing 2004;Chen and Yan 2006;Wang et al 2008;Guo and Zhou 2010;Lü et al 2010;Li et al 2010;Manafian 2016;Khater 2015;Youssoufa et al 2019;Youssoufa et al 2022). Many researchers have applied such methods to various equations, (Khater and Zahran 2016;Wazwaz 2007;Manafian et al 2017;Mirzazadeh et al 2015;Wazwaz and Mehanna 2021;Biswas, Aceves et al 2001;Singh et al 2020;El-Ganaini et al 2015;Ali Faridi et al 2024;Ali Faridi and AlQahtani 2023;Ali Faridi et al 2023;Ali Faridi et al 2023a;Ali Faridi et al 2023b;Zain Majida et al 2023;Hamza Rafiq et al 2023;Kaplan et al 2018;Shakeel et al 2014;Ahmad and Mustafa 2023;Hussain Tipu et al 2024;Rani et al 2022;Rani et al 2020;Aniqa and Ahmad 2022;Ali et al 2023a, b;Ali et al 2023c;…”