TY - JOUR

T1 - Asymptotics for the fractional nonlinear Schrödinger equation with 2<α<52

AU - Hayashi, Nakao

AU - Mendez-Navarro, Jesus A.

AU - Naumkin, Pavel I.

N1 - Funding Information:
We would like to thank the referee for the careful reading and useful suggestions on the draft. The work of N.H. is partially supported by JSPS KAKENHI Grant Numbers JP20K03680, JP19H05597. The work of P.I.N. is partially supported by CONACYT project 283698 and PAPIIT project IN103221.
Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.

PY - 2022/9

Y1 - 2022/9

N2 - We study the Cauchy problem for the fractional nonlinear Schrödinger equation {i∂tu-1α|∂x|αu=λ|u|αu,t>0,x∈R,u(0,x)=u0(x),x∈R,where λ ∈ R, the fractional derivative |∂x|α=F-1|ξ|αF, the order α∈(2,52). Our aim is to find the asymptotics of solutions to the fractional nonlinear Schrödinger equation in the defocusing case λ > 0. We show that the asymptotics differs from that in the case of the usual cubic nonlinear Schrödinger equation. To prove our main result, we develop the Factorization Techniques which was proposed in our previous works.

AB - We study the Cauchy problem for the fractional nonlinear Schrödinger equation {i∂tu-1α|∂x|αu=λ|u|αu,t>0,x∈R,u(0,x)=u0(x),x∈R,where λ ∈ R, the fractional derivative |∂x|α=F-1|ξ|αF, the order α∈(2,52). Our aim is to find the asymptotics of solutions to the fractional nonlinear Schrödinger equation in the defocusing case λ > 0. We show that the asymptotics differs from that in the case of the usual cubic nonlinear Schrödinger equation. To prove our main result, we develop the Factorization Techniques which was proposed in our previous works.

KW - Asymptotics of solutions

KW - Factorization technique

KW - Fractional nonlinear Schrödinger equation

KW - Modified scattering

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U2 - 10.1007/s11868-022-00460-z

DO - 10.1007/s11868-022-00460-z

M3 - Article

AN - SCOPUS:85130971007

SN - 1662-9981

VL - 13

JO - Journal of Pseudo-Differential Operators and Applications

JF - Journal of Pseudo-Differential Operators and Applications

IS - 3

M1 - 30

ER -