The Cauchy problem for a 4-parameter family of equations with peakon traveling waves

DOI10.1016/j.na.2015.12.012zbMath1330.35371OpenAlexW2216667641MaRDI QIDQ2634369

Dionyssios Mantzavinos, A. Alexandrou Himonas

Publication date: 9 February 2016

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2015.12.012

zbMATH Keywords

Cauchy problemapproximate solutionsHölder continuityconserved quantitiesCamassa-Holm equationDegasperis-Procesi equationintegrable equationsNovikov equationwell-posedness in Sobolev spacescommutator estimateFokas-Olver-Rosenau-Qiao equationnon-uniform dependence on initial dataPeakon traveling waves

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) Traveling wave solutions (35C07)

Related Items

Wave breaking phenomenon for the generalized FORQ equation, The power series method for nonlocal and nonlinear evolution equations, A general family of multi-peakon equations and their properties, Nonuniqueness for the \(ab\)-family of equations with peakon travelling waves on the circle, Well-posedness and continuity properties of the new shallow-water model with cubic nonlinearity, A new blow-up criterion for the \(N - abc\) family of Camassa-Holm type equation with both dissipation and dispersion, Conserved norms and related conservation laws for multi-peakon equations, Non-uniqueness for the ab-family of equations, Lax integrability and the peakon problem for the modified Camassa-Holm equation, Curvature blow-up for the higher-order Camassa-Holm equations, The Cauchy problem of a weakly dissipative shallow water equation, Nonuniform dependence and well-posedness for the generalized Camassa–Holm equation, Global well-posedness and infinite propagation speed for the N − abc family of Camassa–Holm type equation with both dissipation and dispersion, Decay properties of solutions to a 4-parameter family of wave equations, Persistent decay of solutions to the \(k- abc\) equation in weighted \(L^p\) spaces, An 𝑎𝑏-family of equations with peakon traveling waves, Lax Integrability of the Modified Camassa-Holm Equation and the Concept of Peakons, Blow-up and peakons for a higher-order \(\mu\)-Camassa-Holm equation

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