The "good" Boussinesq equation: a Riemann-Hilbert approach

DOI10.1512/iumj.2022.71.8981zbMath1502.35074arXiv2003.02777OpenAlexW3009051369WikidataQ114053249 ScholiaQ114053249MaRDI QIDQ5050604

Jonatan Lenells, Christophe Charlier

Publication date: 17 November 2022

Published in: Indiana University Mathematics Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2003.02777

zbMATH Keywords

inverse scattering transformBoussinesq equationRiemann-Hilbert probleminitial value problemspectral analysis

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) PDEs in connection with fluid mechanics (35Q35) Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Initial value problems for nonlinear higher-order PDEs (35G25) Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15) Riemann-Hilbert problems in context of PDEs (35Q15)

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Long-time asymptotics of the good Boussinesq equation with q xx-term and its modified version, Long-time asymptotic behavior for the matrix modified Korteweg-de Vries equation, Inverse scattering transform for the two‐component Gerdjikov–Ivanov equation with nonzero boundary conditions: Dark‐dark solitons, Soliton resolution and large time behavior of solutions to the Cauchy problem for the Novikov equation with a nonzero background, Asymptotic stability manifolds for solitons in the generalized good Boussinesq equation, The ``good Boussinesq equation: long-time asymptotics

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