典型文献
Long-time Asymptotic Behavior for the Derivative Schr?dinger Equation with Finite Density Type Initial Data
文献摘要：
In this paper,the authors apply(?)steepest descent method to study the Cauchy problem for the derivative nonlinear Schr?dinger equation with finite density type initial data iqt+qxx+i(|q|2q)x=0,q(x,0)=q0(x),where lim x→±∞ q0(x)=q±and|q±|=1.Based on the spectral analysis of the Lax pair,they express the solution of the derivative Schr?dinger equation in terms of solutions of a Riemann-Hilbert problem.They compute the long time asymptotic expansion of the solution q(x,t)in different space-time regions.For the region ξ=x/t with|ξ+2|＜1,the long time asymptotic is given by q(x,t)=T(∞)-2qrΛ(x,t)+O(t-3/4),in which the leading term is N(I)solitons,the second term is a residual error from a(?)equation.For the region |ξ+2|＞1,the long time asymptotic is given by q(x,t)=T(∞)-2qrΛ(x,t)-t-1/2if11+O(t-3/4),in which the leading term is N(I)solitons,the second t-1/2 order term is soliton-radiation interactions and the third term is a residual error from a(?)equation.These results are verification of the soliton resolution conjecture for the derivative Schr?dinger equation.In their case of finite density type initial data,the phase function θ(z)is more complicated that in finite mass initial data.Moreover,two triangular decompositions of the jump matrix are used to open jump lines on the whole real axis and imaginary axis,respectively.
文献关键词：
中图分类号：
作者姓名：
Yiling YANG;Engui FAN
作者机构：
School of Mathematical Sciences,Fudan University,Shanghai 200433,China
文献出处：
引用格式：
[1]Yiling YANG;Engui FAN-.Long-time Asymptotic Behavior for the Derivative Schr?dinger Equation with Finite Density Type Initial Data)[J].数学年刊B辑（英文版）,2022(06):893-948
A类：
iqt+qxx+i,2qr,2if11+O
B类：
Long,Asymptotic,Behavior,Derivative,Schr,dinger,Equation,Finite,Density,Type,Initial,Data,this,paper,authors,apply,steepest,descent,method,study,Cauchy,problem,derivative,nonlinear,equation,finite,density,type,initial,data,q0,where,lim,Based,spectral,analysis,Lax,pair,they,express,terms,solutions,Riemann,Hilbert,They,compute,long,asymptotic,expansion,different,space,regions,For,+2,given,by,which,leading,solitons,second,residual,error,from,order,radiation,interactions,third,These,results,are,verification,resolution,conjecture,their,case,phase,function,more,complicated,that,mass,Moreover,two,triangular,decompositions,jump,matrix,used,open,lines,whole,real,axis,imaginary,respectively
AB值：
0.500625
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