Korteweg-de Vries–modified Korteweg-de Vries systems and Darboux transforms in 1+1 and 2+1 dimensions

DOI10.1063/1.530165zbMath0774.35075OpenAlexW2042170631MaRDI QIDQ4201712

Sergiej B. Leble, Nikolai V. Ustinov

Publication date: 6 September 1993

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

Full work available at URL: https://doi.org/10.1063/1.530165

zbMATH Keywords

solitonslocalized solutionsJaulent-Miodek hierarchy

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Geometric theory, characteristics, transformations in context of PDEs (35A30) Correspondences and other transformation methods (e.g., Lie-Bäcklund) for PDEs on manifolds (58J72)

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Cites Work

• Darboux transformation and explicit solutions of the Kadomtsev-Petviashvili equation, depending on functional parameters
• Coupled KdV equations with multi-Hamiltonian structures
• Nonlinear evolution equations associated with energy-dependent Schrödinger potentials
• Mathematics of dispersive water waves
• On a new hierarchy of Hamiltonian soliton equations
• A hierarchy of coupled Korteweg-de Vries equations and the normalisation conditions of the Hilbert-Riemann problem
• Generalised KdV and MKdV equations associated with symmetric spaces
• Schrödinger spectral problems with energy–dependent potentials as sources of nonlinear Hamiltonian evolution equations