A direct method for dromion solutions of the Davey-Stewartson equations and their asymptotic properties

DOI10.1098/rspa.1991.0148zbMath0743.35074OpenAlexW2117959659MaRDI QIDQ3982083

Claire R. Gilson, Jonathan J. C. Nimmo

Publication date: 26 June 1992

Published in: Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1098/rspa.1991.0148

zbMATH Keywords

asymptotic analysisDavey-Stewartson equationsinteractionphase shiftschanges of amplitudedromion scattering

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Soliton equations (35Q51) Soliton solutions (35C08)

Related Items (18)

Soliton resonance and web structure in the Davey–Stewartson system ⋮ Self-consistent sources for integrable equations via deformations of binary Darboux transformations ⋮ New symmetry reductions and exact solutions of the Davey–Stewartson system. I. Reductions to ordinary differential equations ⋮ Soliton solutions of the Hamiltonian DSI and DSIII equations ⋮ New exact solutions of Burgers’s equation—an extension to the direct method of Clarkson and Kruskal ⋮ Dromions bound states. ⋮ Deformation of the dromion and solitoff solutions of the Davey-Stewartson I equation ⋮ Darboux transformations for the Davey-Stewartson equations ⋮ Source generation of the Davey-Stewartson equation ⋮ Dromions of flexural-gravity waves ⋮ The Davey-Stewartson equation and constrained linear flows ⋮ On a structure of the explicit solutions to the Davey-Stewartson equations ⋮ Hirota’s Bilinear Method and Its Connection with Integrability ⋮ Localized coherent structures and integrability in a generalized \((2+1)\)-dimensional nonlinear Schrödinger equation ⋮ Extended Gram-type determinant solutions to the Kadomtsev-Petviashvili equation ⋮ Lax pairs and Bäcklund transformations for a coupled Ramani equation and its related system ⋮ Soliton solutions and Bäcklund transformation for the Kupershmidt five-field lattice: A bilinear approach ⋮ Multidimensional localized solitons.

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