On the asymptotic stability of \(N\)-soliton solution for the short pulse equation with weighted Sobolev initial data
DOI10.1016/j.jde.2023.08.028zbMath1527.35194MaRDI QIDQ6084163
Shou-Fu Tian, Zhi-Qiang Li, Jin-Jie Yang
Publication date: 31 October 2023
Published in: Journal of Differential Equations (Search for Journal in Brave)
asymptotic stabilityRiemann-Hilbert problemintegrable systemshort pulse equationsoliton resolution\(\bar{\partial}\)-steepest descent method
Asymptotic behavior of solutions to PDEs (35B40) PDEs in connection with fluid mechanics (35Q35) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Stability in context of PDEs (35B35) Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) NLS equations (nonlinear Schrödinger equations) (35Q55) Asymptotic expansions of solutions to PDEs (35C20) Soliton equations (35Q51) Lasers, masers, optical bistability, nonlinear optics (78A60) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Riemann-Hilbert problems in context of PDEs (35Q15) Soliton solutions (35C08) Time-dependent Schrödinger equations and Dirac equations (35Q41) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)
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