Looking at an open sea via a generalized -dimensional dispersive long-wave system for the shallow water: scaling transformations, hetero-Bäcklund transformations, bilinear forms and N solitons
State Key Laboratory of Information Photonics and Optical Communications, and School of Science, Beijing University of Posts and Telecommunications, 100876, Beijing, China
Accepted: 18 July 2021
Published online: 31 August 2021
Oceanic water-wave studies are attractive. Hereby, with a view to modelling the nonlinear and dispersive long gravity waves in two horizontal directions on the shallow water of an open sea or a wide channel of finite depth, we inquire into a generalized (2+1)-dimensional dispersive long-wave system, by virtue of the scaling transformations we hereby obtain, Bell polynomials and symbolic computation. As for the horizontal velocity and wave elevation above the undisturbed water surface, we find two branches of the hetero-Bäcklund transformations, two branches of the bilinear forms and two branches of the N-soliton solutions, with N as a positive integer. What we have obtained relies on the coefficients in the system.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2021