The KdV equation under periodic boundary conditions and its perturbations

DOI10.1088/0951-7715/27/9/R61zbMath1301.35132arXiv1309.1597MaRDI QIDQ2924831

Huang Guan, Sergej B. Kuksin

Publication date: 17 October 2014

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1309.1597

zbMATH Keywords

random perturbationaveragingKdVKolmogorov-Arnold-Moser (KAM)perturbed KdV

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) KdV equations (Korteweg-de Vries equations) (35Q53) Long-time behavior of solutions for dynamical problems in solid mechanics (74H40) Perturbations, KAM theory for infinite-dimensional Hamiltonian and Lagrangian systems (37K55) Averaging of perturbations for nonlinear problems in mechanics (70K65)

Related Items (11)

KAM for autonomous quasi-linear perturbations of mKdV ⋮ Boundary integral methods for dispersive equations, Airy flow and the modified Korteweg de Vries equation ⋮ Construction of quasi-periodic solutions for nonlinear forced perturbations of dissipative Boussinesq systems ⋮ KdV Hamiltonian as a function of actions ⋮ Real analytic quasi-periodic solutions with more Diophantine frequencies for perturbed KdV equations ⋮ Invariant tori of full dimension for second KdV equations with the external parameters ⋮ Energy-conserving Hamiltonian boundary value methods for the numerical solution of the Korteweg-de Vries equation ⋮ Quasi-periodic solutions for quasi-linear generalized KdV equations ⋮ Long time dynamics for generalized Korteweg-de Vries and Benjamin-Ono equations ⋮ On the convexity of the KdV Hamiltonian ⋮ On longtime dynamics of perturbed KdV equations

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