Asymptotic behavior of solutions to the short pulse equation with critical nonlinearity

DOI10.1016/j.na.2014.08.008zbMath1301.35138OpenAlexW2018054149MaRDI QIDQ744148

Tomoyuki Niizato

Publication date: 6 October 2014

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.2014.08.008

zbMATH Keywords

asymptotic behavior of solutionsscattering problemtime decay estimateshort pulse equation

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) PDEs in connection with optics and electromagnetic theory (35Q60) KdV equations (Korteweg-de Vries equations) (35Q53) Diffraction, scattering (78A45) A priori estimates in context of PDEs (35B45) Existence problems for PDEs: global existence, local existence, non-existence (35A01)

Related Items

The short pulse equation by a Riemann-Hilbert approach ⋮ Large time asymptotics of solutions to the short-pulse equation ⋮ Large time asymptotics for the reduced Ostrovsky equation

Cites Work

• A new proof of long-range scattering for critical nonlinear Schrödinger equations.
• Nonlinear fractional Schrödinger equations in one dimension
• Well-posedness and small data scattering for the generalized Ostrovsky equation
• Wave breaking in the short-pulse equation
• Propagation of ultra-short optical pulses in cubic nonlinear media
• Asymptotics of solutions to the generalized Ostrovsky equation
• Existence globale et comportement asymptotique pour l'équation de Klein–Gordon quasi linéaire à données petites en dimension 1
• Global Well-Posedness of the Short-Pulse and Sine–Gordon Equations in Energy Space
• Asymptotics for large time of solutions to the nonlinear Schrodinger and Hartree equations
• Large time asymptotics of solutions to the generalized Benjamin-Ono equation
• Nonexistence of the usual scattering states for the generalized Ostrovsky-Hunter equation
• Ostrovsky and Hunter's generic wave equation for weakly dispersive waves: matched asymptotic and pseudospectral study of the paraboloidal travelling waves (corner and near-corner waves)
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item