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تسجيل مستخدم جديدLong-time asymptotic behavior of the nonlocal nonlinear Schrodinger equation with initial potential in weighted sobolev space
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In this paper, we are going to investigate Cauchy problem for nonlocal nonlinear Schrodinger equation with the initial potential $q_0(x)$ in weighted sobolev space $H^{1,1}(mathbb{R})$, begin{align*} iq_t(x,t)&+q_{xx}(x,t)+2sigma q^2(x,t)bar q(-x,t)=0,quadsigma=pm1, q(x,0)&=q_0(x). end{align*} We show that the solution can be represented by the solution of a Riemann-Hilbert problem (RH problem), and assuming no discrete spectrum, we majorly apply $barpartial$-steepest cescent descent method on analyzing the long-time asymptotic behavior of it.
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