New Soliton Solutions and Soliton Evolvements for(2+1)-Dimensional Dispersive Long Wave Equation

Letter to the Editor: Thinking of the oceanic shallow water in the light of a (2+1)-dimensional generalized dispersive long-wave system related to HFF 33, 3272; 33, 965 and 32, 2282

“…which has some special cases in hydrodynamics (Boiti et al, 1987;Tian and Gao, 1996;Gramolin, 2008, 2009;Wen, 2009;Sun et al, 2010;Hu et al, 2016;Xia et al, 2017;Yang and Feng, 2018), with d = 0, b and a = 0 standing for three real constants, the horizontal velocity, u(x, y, t), and the wave height above the undisturbed water surface, v(x, y, t), being two real differentiable functions with respect to the variables t, x and y, (x, y) representing the propagation plane while t implying the time. For system (1), certain similarity reductions (Gao et al, 2022b(Gao et al, , 2023a(Gao et al, , 2021b, hetero-Bäcklund transformations (Gao et al, 2023a(Gao et al, , 2021c(Gao et al, , 2020, bilinear forms (Gao et al, 2022b(Gao et al, , 2021c, scaling transformations (Gao et al, 2021c), solitons (Gao et al, 2021c(Gao et al, , 2020 and auto-Bäcklund transformations (Gao et al, 2020) have been reported.…”

“…Getting enthusiastic from Liu (2023), Khuri (2023) and Li et al (2022), this Letter designs to symbolically compute a (2+1)-dimensional generalized dispersive long-wave system modeling certain dispersive and nonlinear long gravity waves in two directions, horizontally, on the shallow water of an ocean (Gao et al , 2022b, 2023a, 2021b, 2021c, 2020), i.e. : which has some special cases in hydrodynamics (Boiti et al ., 1987; Tian and Gao, 1996; Dubrovsky and Gramolin, 2008, 2009; Wen, 2009; Sun et al ., 2010; Hu et al ., 2016; Xia et al ., 2017; Yang and Feng, 2018), with δ ≠ 0, β and α ≠ 0 standing for three real constants, the horizontal velocity, u ( x , y , t ), and the wave height above the undisturbed water surface, v ( x , y , t ), being two real differentiable functions with respect to the variables t , x and y , ( x , y ) representing the propagation plane while t implying the time. For system (1), certain similarity reductions (Gao et al , 2022b, 2023a, 2021b), hetero-Bäcklund transformations (Gao et al , 2023a, 2021c, 2020), bilinear forms (Gao et al , 2022b, 2021c), scaling transformations (Gao et al , 2021c), solitons (Gao et al , 2021c, 2020) and auto-Bäcklund transformations (Gao et al , 2020) have been reported.…”