Long-time asymptotic behavior for the nonlocal nonlinear Schrödinger equation in the solitonic region  

作　　者：Gaozhan Li Yiling Yang Engui Fan 

机构地区：[1]School of Mathematical Sciences and Key Laboratory of Mathematics for Nonlinear Sciences,Fudan University,Shanghai 200433,China

出　　处：《Science China Mathematics》2025年第2期379-398,共20页中国科学(数学英文版)

基　　金：supported by National Natural Science Foundation of China(Grant Nos.12271104,51879045,12247182).

摘　　要：In this paper,we extend the δ^(-)-steepest descent method to study the Cauchy problem for the nonlocal nonlinear Schrödinger(NNLS)equation with weighted Sobolev initial data iqt+qxx+2σq^(2)(x,t)q(−x,t)=0,q(x,0)=q0(x),where q0∈H^(1,1)(R).Based on the spectral analysis of the Lax pair,the solution of the Cauchy problem is expressed in terms of the solution of a Riemann-Hilbert problem,which is transformed into a solvable model after a series of deformations.We further obtain the asymptotic expansion of the solution to the Cauchy problem for the NNLS equation in the solitonic region.The leading term is soliton solutions,the second term is the interaction between solitons and dispersion,and the error term comes from a corresponding δ^(-)-problem.Compared with the asymptotic results on the classical NLS equation,the major difference is the second and third terms of the asymptotic expansion for the NNLS equation,which were affected by a function depending on the scattering data and the stationary phase point.

关 键 词：nonlocal nonlinear Schrödinger equation Riemann-Hilbert problem δ^(-)-steepest descent method soliton resolution 

分 类 号：O175.2[理学—数学]