The ∂̄-dressing method for the (2+1)-dimensional Jimbo-Miwa equation

DOI10.1090/proc/15716zbMath1495.37059OpenAlexW3174930944MaRDI QIDQ5081518

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Publication date: 15 June 2022

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/proc/15716

zbMATH Keywords

Green's functioncharacteristic functionJimbo-Miwa equation\(\bar{\partial}\)-dressing methodinverse spectral transformation

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Inverse problems for PDEs (35R30) Soliton equations (35Q51) Geometric theory, characteristics, transformations in context of PDEs (35A30) Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15)

Related Items (2)

The \(\bar{\partial}\)-dressing method for the (2+1)-dimensional Konopelchenko-Dubrovsky equation ⋮ \( \bar{\partial } \)-dressing method for a generalized \((2 + 1)\)-dimensional nonlinear wave equation

Cites Work

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• The higher-order soliton solutions for the coupled Sasa-Satsuma system via the \(\overline{\partial}\)-dressing method
• Solitons and infinite dimensional Lie algebras
• A dressing method in mathematical physics.
• Bäcklund transformations and their applications
• The dressing method and nonlocal Riemann-Hilbert problems
• Multi-soliton solutions of KP equation with integrable boundary via \(\overline{\partial}\)-dressing method
• Long-time asymptotics for the Fokas-Lenells equation with decaying initial value problem: without solitons
• Cusp solitons to the long-short waves equation and the \(\bar{\partial}\)-dressing method
• A steepest descent method for oscillatory Riemann-Hilbert problems. Asymptotics for the MKdV equation
• Painlevé test for some \((2+1)\)-dimensional nonlinear equations
• The generalized dressing method with applications to variable-coefficient coupled Kadomtsev-Petviashvili equations
• On the Inverse Scattering Transform for the Kadomtsev-Petviashvili Equation
• Exact Solution of the Korteweg—de Vries Equation for Multiple Collisions of Solitons
• The Painlevé property for partial differential equations
• The application of the -dressing method to some integrable -dimensional nonlinear equations
• A hierarchy of coupled evolution equations with self-consistent sources and the dressing method
• Darboux Transformations
• Exact envelope-soliton solutions of a nonlinear wave equation

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