The ∂̄-dressing method and the solutions with constant asymptotic values at infinity of DS-II equation

DOI10.1063/1.532218zbMath0898.58028OpenAlexW1975159402MaRDI QIDQ4384785

V. G. Dubrovskij

Publication date: 26 April 1998

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.532218

zbMATH Keywords

exact solutionsrational solutionsDavey-Stewartson equationfunctional parameters\(\overline{\partial}\)-dressing methodconstant asymptotic values at infinityDS-II equationmulti-line solitons

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) NLS equations (nonlinear Schrödinger equations) (35Q55) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35)

Related Items

Punctures for theories of class \( {\mathcal{S}}_{\Gamma} \) ⋮ Nonlinear Schrödinger equation with nonzero boundary conditions revisited: Dbar approach ⋮ The ∂̄-dressing method and soliton solutions for the three-component coupled Hirota equations ⋮ Quarter-BPS states in orbifold sigma models with ADE singularities ⋮ On the \(\bar\partial \)-problem and dressing method for the complex vector modified KdV equation

Cites Work

• Inverse scattering transform method and soliton solutions for Davey- Stewartson II equation
• The Davey-Stewartson equation and constrained linear flows
• On a structure of the explicit solutions to the Davey-Stewartson equations
• Construction of higher-dimensional nonlinear integrable systems and of their solutions
• Multi-scale expansions in the theory of systems integrable by the inverse scattering transform
• A scheme for integrating the nonlinear equations of mathematical physics by the method of the inverse scattering problem. I
• Finite-gap solutions of the Davey-Stewartson equations
• The dressing method and nonlocal Riemann-Hilbert problems
• On the inverse scattering transform of multidimensional nonlinear equations related to first-order systems in the plane
• The non-local delta problem and (2+1)-dimensional soliton equations
• Two-dimensional lumps in nonlinear dispersive systems
• On the soliton solutions of the Davey-Stewartson equation for long waves
• The application of the -dressing method to some integrable -dimensional nonlinear equations
• On three-dimensional packets of surface waves
• Finite-rank constraints on linear flows and the Davey-Stewartson equation
• Wave Instabilities