Asymptotics for the third‐order nonlinear Schrödinger equation in the critical case | Zendy

Hayashi Nakao | Zendy; Kaikina Elena I. | Zendy

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Asymptotics for the third‐order nonlinear Schrödinger equation in the critical case

Author(s) -

Hayashi Nakao,

Kaikina Elena I.

Publication year - 2016

Publication title -

mathematical methods in the applied sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.719

H-Index - 65

eISSN - 1099-1476

pISSN - 0170-4214

DOI - 10.1002/mma.4080

Subject(s) - mathematics , nonlinear schrödinger equation , nonlinear system , fourier transform , initial value problem , order (exchange) , logarithm , mathematical analysis , third order , zero (linguistics) , cauchy problem , schrödinger equation , split step method , mathematical physics , partial differential equation , physics , quantum mechanics , law , linguistics , philosophy , political science , finance , economics

We consider the Cauchy problem for the third‐order nonlinear Schrödinger equation where ℋ = F − 1 iξξ− 1 F and F is the Fourier transform. Our purpose in this paper is to prove the large time asymptoitic behavior of solutions for the defocusing case λ > 0 with a logarithmic correction under the non zero mass condition ∫ u 0x dx ≠ 0 . Copyright © 2016 John Wiley & Sons, Ltd.

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