Oceanic Shallow-Water Investigations on a Variable-Coefficient Davey–Stewartson System

Haoqing Chen, Guangmei Wei (), Yuxin Song and Yaqin Xie
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Haoqing Chen: School of Mathematical Sciences, Beihang University, Beijing 100191, China
Guangmei Wei: School of Mathematical Sciences, Beihang University, Beijing 100191, China
Yuxin Song: School of Mathematical Sciences, Beihang University, Beijing 100191, China
Yaqin Xie: School of Mathematical Sciences, Beihang University, Beijing 100191, China

Mathematics, 2024, vol. 12, issue 11, 1-15

Abstract: In this paper, a variable-coefficient Davey–Stewartson (vcDS) system is investigated for modeling the evolution of a two-dimensional wave-packet on water of finite depth in inhomogeneous media or nonuniform boundaries, which is where its novelty lies. The Painlevé integrability is tested by the method of Weiss, Tabor, and Carnevale (WTC) with the simplified form of Krustal. The rational solutions are derived by the Hirota bilinear method, where the formulae of the solutions are represented in terms of determinants. Furthermore the fundamental rogue wave solutions are obtained under certain parameter restrains in rational solutions. Finally the physical characteristics of the influences of the coefficient parameters on the solutions are discussed graphically. These rogue wave solutions have comprehensive implications for two-dimensional surface water waves in the ocean.

Keywords: Davey–Stewartson equation; Painlevé property; rational solution; rogue-wave solution; symbolic computation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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