Peculiar optical solitons and modulated waves patterns in anti-cubic nonlinear media with cubic–quintic nonlinearity

New computational approaches to the fractional coupled nonlinear Helmholtz equation

“…, 2013; Seadawy, 2014; Iqbal et al. , 2019; Houwe et al. , 2023), and the Multi-Scale transform scheme (Ain et al.…”

“…The classical coupled nonlinear Helmholtz (CCNH) equation is stated as Singh et al (2020) In recent years, the exploration of soliton solutions in nonlinear evolution equations has gained significant traction among mathematicians and physicists, thus prompting the development of numerous excellent and effective methods. These include the sub-equation method (Duran and Kaya, 2021), generalized exponential rational function technique (Duran, 2021a;Seadawy et al, 2020), Hirota bilinear method (zvi et al, 2020, direct algebraic method (Seadawy et al, 2013;Seadawy, 2014;Iqbal et al, 2019;Houwe et al, 2023), and the Multi-Scale transform scheme (Ain et al, 2021(Ain et al, , 2022. Other methods that have gained recognition are the wavelet collocation method (Yadav et al, 2023), Unified method (Seadawy et al, 2021), Lie symmetry analysis approach (Kumar et al, 2023;Kumar and Kumar, 2019), Variational method (Nadeem et al, 2009), exp-function method (Raheel et al, 2023;Batool et al, 2024;Abde et al, 2019), (G 0 /G)-expansion scheme (Duran, 2021b), Modified Kudryashov method (Akbulut et al, 2023), Symmetry group method (Liu et al, 2022), among others (Seadawy et al, 2019;Kumar et al, 2020;Ahmad et al, 2020;Seadawy and Ali, 2023;Akbulut et al, 2017;Rizvi et al, 2021;Khater, 2022;Wang, 2024a, b, c, d, e, f;Ghanbari et al, 2022;Ozkan, 2022;Fendzi-Donfack et al, 2021).…”