Considering the wave processes in oceanography, acoustics and hydrodynamics by means of an extended coupled (2+1)-dimensional Burgers system

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

“…Towards system (1), similar to those in Clarkson and Kruskal (1989), Gao and Tian (2022, 2024) as well as Gao (2023, 2024b, 2024c), the assumptions and choice of z y z t ≠ 0 develop into with θ ( x , y , t ), ω ( x , y , t ), ≠ 0, γ ( x , y , t ), κ ( x , y , t ) ≠ 0 and z ( y , t ) ≠ 0 meaning certain real to-be-determined differentiable functions, p ( z ) and q ( z ) denoting two real differentiable functions while the “′” sign representing d/d z .…”

“…Towards system (1), similar to those in Clarkson and Kruskal (1989), Tian (2022, 2024) as well as Gao (2023Gao ( , 2024bGao ( , 2024c, the assumptions…”

Analytic soliton solutions to the shallow water dispersive long gravity wave equations: the first integral approach in nonlinear physics

“…Gao [11] explored the (3+1)-dimensional generalized Yu-Toda-Sasa-Fukuyama system by constructing a series of similarity reductions. Gao [12] also constructed two sets of hetero-Bäcklund transformations, which are associated with the system of (2+1)-dimensional Broer-Kaup-Kupershmidt equations and a set of similarity reductions. In nonlinear sciences there are three key concepts, namely fractal, soliton, and chaos.…”

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

“…For the sake of constructing certain similarity reductions for equation ( 1), similar to those in Clarkson and Kruskal (1989); Gao (2023bGao ( , 2024a; and Gao and Tian (2024), the form of f(x, t) can be assumed as:…”

“…For the sake of constructing certain similarity reductions for equation (1), similar to those in Clarkson and Kruskal (1989); Gao (2023b, 2024a); and Gao and Tian (2024), the form of ϕ ( χ , τ ) can be assumed as: of which α ( χ , τ ), β ( χ , τ ) ≠ 0 and w ( χ , τ ) ≠ 0 represent some real differentiable functions to be determined while r ( w ) denotes a real differentiable function as for w only.…”