Ultra-short optical pulses in a birefringent fiber via a generalized coupled Hirota system with the singular manifold and symbolic computation

Letter to the Editor on HFF 32, 138 (2022); 32, 2282 (2022); 33, 965 (2023) and 34, 1189 (2024) for the recent shallow-water studies

“…in which the real differentiable functions v(x, y, t) and u(x, y, t), respectively, imply the horizontal velocity of the water wave and the height of the water surface, a and b are the real non-zero constants, and the subscripts represent the partial derivatives concerning the scaled space variables x, y and time variable t. With symbolic computation (Anderson and Farazmand, 2024;Kovacs et al, 2024;Shen et al, 2023aShen et al, , 2023bGao et al, 2023b;Wu and Gao, 2023;Wu et al, 2023aWu et al, , 2023cWu et al, , 2023dZhou and Tian, 2022) in planning, Gao et al (2023a) have given a set of the hetero-Bäcklund transformations, a set of the scaling transformations and four sets of the similarity reductions for system (1), whereas Liu et al (2023) have investigated certain Lie point symmetry generators, Lie symmetry groups and symmetry reductions for system (1) with some analytic solutions. Shallow-water special cases of system (1) have been seen in Ying and Lou (2000), Li and Zhang (2004), Ma et al (2015), Zhao and Han (2015), Kassem and Rashed (2019), (2022), Gao et al (2023a) as well as Liu et al (2023).…”

“…Enthusiasm for the shallow water has been warmed by Wazwaz (2022), Li et al (2022), Khuri (2023) and Ramos and Garcia Lopez (2024), and consequently this shallow-water-oriented Letter aims to deal with a (2+1)-dimensional generalised modified dispersive water-wave system for the nonlinear and dispersive long gravity waves travelling along two horizontal directions in the shallow water of uniform depth (Gao et al , 2023a; Liu et al , 2023): in which the real differentiable functions v ( x , y , t ) and u ( x , y , t ), respectively, imply the horizontal velocity of the water wave and the height of the water surface, α and β are the real non-zero constants, and the subscripts represent the partial derivatives concerning the scaled space variables x , y and time variable t . With symbolic computation (Anderson and Farazmand, 2024; Kovacs et al , 2024; Shen et al , 2023a, 2023b, 2023e, 2023f; Gao et al , 2023b; Wu and Gao, 2023; Wu et al , 2023a, 2023c, 2023d; Zhou and Tian, 2022) in planning, Gao et al (2023a) have given a set of the hetero-Bäcklund transformations, a set of the scaling transformations and four sets of the similarity reductions for system (1), whereas Liu et al (2023) have investigated certain Lie point symmetry generators, Lie symmetry groups and symmetry reductions for system (1) with some analytic solutions. Shallow-water special cases of system (1) have been seen in Ying and Lou (2000), Li and Zhang (2004), Ma et al .…”

Letter to the editor: Discussing some Korteweg-de Vries-directional contributions in fluid mechanics, atmospheric science, plasma physics and nonlinear optics concerning HFF 33, 3111 and 32, 1674

“…Special cases of equation ( 1) have been seen in fluid mechanics, atmospheric science, plasma physics and nonlinear optics (Brugarino, 1989;Kapadia, 2001;Zhang et al, 2013;Chen et al, 2020aChen et al, , 2020b. By the way, other nonlinear models in fluid mechanics, atmospheric science, plasma physics and nonlinear optics have also been presented (Chen et al, 2024a(Chen et al, , 2024bPeng et al, 2024;Cheng et al, 2022Cheng et al, , 2023aCheng et al, , 2023bGao, 2023aGao, , 2024bGao, , 2024cGao et al, 2023aGao et al, , 2023bWu and Gao, 2023;Wu et al, 2023aWu et al, , 2023bShen et al, 2023aShen et al, , 2023bShen et al, , 2023cZhou and Tian, 2022;Zhou et al, 2023aZhou et al, , 2023bFeng et al, 2023).…”