Large time asymptotics of solutions to the short-pulse equation

DOI10.1007/S00030-017-0464-8zbMath1375.35456arXiv1612.07869OpenAlexW2951113506MaRDI QIDQ2411110

Mamoru Okamoto

Publication date: 20 October 2017

Published in: NoDEA. Nonlinear Differential Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1612.07869

zbMATH Keywords

short-pulse equationreduced Ostrovsky equationmodified scattering

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) Scattering theory for PDEs (35P25) Lasers, masers, optical bistability, nonlinear optics (78A60)

Related Items (2)

Soliton resolution for the short-pulse equation ⋮ Long-time behavior of solutions to a fourth-order nonlinear Schrödinger equation with critical nonlinearity

Cites Work

• Unnamed Item
• Well-posedness and small data scattering for the generalized Ostrovsky equation
• Asymptotic behavior of solutions to the short pulse equation with critical nonlinearity
• Wave breaking in the short-pulse equation
• Propagation of ultra-short optical pulses in cubic nonlinear media
• Large time asymptotics for the reduced Ostrovsky equation
• Asymptotics of solutions to the generalized Ostrovsky equation
• Long time behavior of solutions to the mKdV
• Wave Breaking in the Ostrovsky–Hunter Equation
• Global bounds for the cubic nonlinear Schrödinger equation (NLS) in one space dimension
• Global Well-Posedness of the Short-Pulse and Sine–Gordon Equations in Energy Space
• Global existence of small amplitude solutions to nonlinear klein-gordon equations in four space-time dimensions
• The Lifespan of Small Data Solutions to the KP-I
• 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)
• Two dimensional water waves in holomorphic coordinates II: global solutions

This page was built for publication: Large time asymptotics of solutions to the short-pulse equation