论文标题
在使用逐步的初始数据的散焦MKDV方程的大型渐近学上
On the large-time asymptotics of the defocusing mKdV equation with step-like initial data
论文作者
论文摘要
它与散落的korteweg-de vries（MKDV）方程相关的是cauchy问题的大渐近学问题，具有逐步的初始数据，即紧凑扰动，即\ begin \ begin {align*} q_ {0}（x）-q_ {0c}（x）= 0，\ \ text {for} \ | x |> n \ end en \ end {align {align*}带有一些正$ n $ q_ {0c}（x）= \ left \ { \ begin {Aligned} ＆c_ {l}，\ quad x \ leqslant 0， ＆c_ {r}，\ quad x> 0， \ end {Aligned} \正确的。 \ end {align*}和$ c_l> c_l> c_ {r}> 0 $。从标准的直接和反向散射理论来看，构建了类似阶梯问题的RH表征。通过执行非线性最陡的下降分析，我们主要在$（x，t）$ - 半平面中的四个渐近区域中的每个渐近区域中的每个渐近区。
It is concerned with the large-time asymptotics of the Cauchy problem of the defocusing modified Korteweg-de Vries (mKdV) equation with step-like initial data subject to compact perturbations, that is, \begin{align*} q_{0}(x)-q_{0c}(x)=0, \ \text{for} \ |x|>N \end{align*} with some positive $N$, where \begin{align*} q_{0c}(x)=\left\{ \begin{aligned} &c_{l}, \quad x\leqslant 0, &c_{r}, \quad x>0, \end{aligned} \right. \end{align*} and $c_l>c_{r}>0$. It follows from the standard direct and inverse scattering theory that an RH characterization for the step-like problem is constructed. By performing the nonlinear steepest descent analysis, we mainly derive the large-time asymptotics in the each of four asymptotic zones in the $(x,t)$-half plane.
