Nonlinearization of spectral problems for the perturbation KdV systems

DOI10.1016/S0378-4371(00)00592-6zbMath0978.35050OpenAlexW2008063887WikidataQ126458323 ScholiaQ126458323MaRDI QIDQ5936858

Wen-Xiu Ma, Ruguang Zhou

Publication date: 9 July 2001

Published in: Physica A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0378-4371(00)00592-6

zbMATH Keywords

finite-dimensional integrable Hamiltonian systemsLiouville integrabilityspectral parameter functional gradient

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) General topics in linear spectral theory for PDEs (35P05) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35)

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Cites Work

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• Nonlinearization of the Lax system for AKNS hierarchy
• Explicit and exact solutions to a Kolmogorov-Petrovskii-Piskunov equation
• Perturbations on the K-dV Solitons –An Approach Based on the Multiple Time Scale Expansion–
• Complete integrability of the Kortweg-de Vries equation under perturbation around its solution: Lie-Backlund symmetry approach
• Hamiltonian perturbation theory and water waves
• Restricted flows of soliton hierarchies: coupled KdV and Harry Dym case
• A Green’s function for a linear equation associated with solitons
• Relation between the Kadometsev–Petviashvili equation and the confocal involutive system
• Soliton Evolution in the Presence of Perturbation
• Integrable couplings of soliton equations by perturbations. I: A general theory and application to the KdV hierarchy

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