具有加权Sobolev空间初值的耦合Kundu-非线性Schrödinger方程的孤子分解  

Soliton resolution of the coupled Kundu-nonlinear Schrödinger equations with the initial data in the weighted Sobolev space

作　　者：杨金杰 田守富 李志强 Jinjie Yang;Shoufu Tian;Zhiqiang Li

机构地区：[1]中国矿业大学数学学院,徐州221116

出　　处：《中国科学：数学》2023年第9期1195-1212,共18页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:11975306);江苏省自然科学基金(批准号:BK20181351和BK20181351);中国国家外联项目(批准号:G2021142002);中央大学基础科研基金(批准号:2019ZDPY07);江苏省“六大人才高峰”高层次人才项目(批准号:JY-059)资助项目。

摘　　要：通过发展■-非线性速降方法,本文研究Kundu-非线性Schrodinger(Kundu-nonlinear Schrodinger,KN-NLS)方程在t趋向无穷时解的长时间渐近行为.在初值u0(x),v0(x)∈H^(1,1)(R)=H^(1)(R)∩L^(2,1)(R)时,本文证明耦合KN-NLS方程的解可以分解为有限个孤子的和与色散分量.更进一步地,在给定的锥C(x1,x2,v1,v2)={(x,t)∈R^(2):x=x0+vt,x0∈[x1,x2],v∈[v1,v2]}中,本文证明可用锥中有限孤子来逼近N孤子解.本文结果也表明,当初值属于加权Sobolev空间时,耦合KN-NLS方程的孤子分解猜想是成立的.In this paper,the■-steepest descent method is developed to investigate the long-time asymptotic behavior of the coupled KN-NLS(Kundu-nonlinear Schrodinger)equations as t tends to in nity.Furthermore,it is proved that for the initial values u0(x),v0(x)2 H^(1,1)(R)=H1(R)\L^(2,1)(R),the evolution for the initial data of the coupled KN-NLS equations is decomposed into the nite soliton and the dispersion radiative component as t!1.Moreover,in the xed space-time cone C(x1,x2,v1,v2)=f(x,t)2 R2:x=x0+vt;x02[x1,x2];v 2[v1,v2]g,we prove that the nite soliton appearing in the cone C(x1;x2,v1,v2)can be used to approximate the N soliton solution.Our results prove the soliton resolution conjecture of the coupled KN-NLS equations with the initial data in the weighted Sobolev space.

关 键 词：耦合Kundu-非线性Schrodinger方程 RIEMANN-HILBERT问题 ■-非线性速降方法 长时间渐近性 孤子分解 

分 类 号：O175[理学—数学]