Inverse Spectral Transform for the Modified Kadomtsev-Petviashvili Equation

DOI10.1002/sapm1992863219zbMath0754.35141OpenAlexW2252559179MaRDI QIDQ3993681

B. G. Konopelchenko, V. G. Dubrovskij

Publication date: 3 August 1992

Published in: Studies in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/sapm1992863219

zbMATH Keywords

exact solutionsMiura transformationbreatherslump solutions\(\overline\partial\)-dressing method

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Riemann-Hilbert problems in context of PDEs (35Q15) Correspondences and other transformation methods (e.g., Lie-Bäcklund) for PDEs on manifolds (58J72)

Related Items (21)

Conservation laws and line soliton solutions of a family of modified KP equations ⋮ Discrete symmetry’s chains and links between integrable equations ⋮ Scheme of constructing soliton-type solutions of the \((2+1)\)-dimensional Harry Dym equation ⋮ Resonance soliton, breather and interaction solutions of the modified Kadomtsev-Petviashvili-II equation ⋮ A \(2+1\) dimensional Volterra type system with nonzero boundary conditions via Dbar dressing method ⋮ Nonlinearly dispersive KP equations with new compacton solutions ⋮ Conservation laws, symmetries, and line soliton solutions of generalized KP and Boussinesq equations with \(p\)-power nonlinearities in two dimensions ⋮ Multisoliton solutions of the \((2+1)\)-dimensional Harry Dym equation ⋮ Bäcklund transformations, rational solutions and soliton-cnoidal wave solutions of the modified Kadomtsev-Petviashvili equation ⋮ Inelastic interactions of the multiple-front waves for the modified Kadomtsev-Petviashvili equation in fluid dynamics, plasma physics and electrodynamics ⋮ On the decomposition of the modified Kadomtsev–Petviashvili equation and explicit solutions ⋮ Soliton solutions of the \((2+1)\)-dimensional Harry Dym equation via Darboux transformation ⋮ Darboux transformation and nonautonomous solitons for a modified Kadomtsev-Petviashvili equation with variable coefficients ⋮ Soliton asymptotics of nondecaying solutions of the modified Kadomtsev–Petviashvili–I equation ⋮ Soliton interaction in the modified Kadomtsev–Petviashvili-(II) equation ⋮ Global well-posedness in the energy space for a modified KP II equation via the Miura transform ⋮ Localized coherent structures of Ishimori equation I through Hirota's bilinearization method: Time dependent/stationary boundaries ⋮ Line-solitons, line-shocks, and conservation laws of a universal KP-like equation in 2+1 dimensions ⋮ Quasilinear systems of Jordan block type and the mKP hierarchy ⋮ Modified Kadomtsev-Petviashvili (MKP) equation and electromagnetic soliton ⋮ Lie symmetry analysis of (2+1)-dimensional KdV equations with variable coefficients

Cites Work

• Solitons and infinite dimensional Lie algebras
• Coherent structures for the Ishimori equation. I: Localized solitons with stationary boundaries
• Hamiltonian methods in the theory of solitons. Transl. from the Russian by A. G. Reyman
• The inverse scattering transform for the time-dependent Schrödinger equation and Kadomtsev-Petviashvili equation
• Construction of higher-dimensional nonlinear integrable systems and of their solutions
• The Modified Korteweg-de Vries Equation
• On the inverse scattering transform of multidimensional nonlinear equations related to first-order systems in the plane
• On the Inverse Scattering Transform for the Kadomtsev-Petviashvili Equation
• On the Inverse Scattering of the Time-Dependent Schrödinger Equation and the Associated Kadomtsev-Petviashvili (I) Equation
• The non-local delta problem and (2+1)-dimensional soliton equations
• A note on Miura’s transformation
• Linear spectral problems, non-linear equations and the δ-method

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