论文标题
带有逐步初始数据的复杂MKDV方程：大渐近分析
The complex mKdV equation with step-like initial data: Large time asymptotic analysis
论文作者
论文摘要
在本文中，我们研究了复杂修改的korteveg-de vries方程\ begin {等式} u_t + _t + \ frac {1} {2} u_ {xxx} +3 | u | u |^2 u_x = 0，\ eent e e e y_t e e e e e e e n e e e e End} u_t vries方程\ frac {1} {2} u_t = 0，与步进的初始数据= 0 {equatization platike}， \ begin {case} 0，＆{x \ ge 0，} \\ a e^{ibx}，＆{x <0.} \ end {cases} \ end {case} \ end {equation}，这表明可以通过matrix riemann-hilbert问题来描述类似阶梯的初始问题。我们采用最陡峭的下降方法来获得Zakharov-Manakov区域，平面波区域和缓慢衰减区域的不同大渐近造物。
In this paper, we study large-time asymptotics for the complex modified Korteveg-de Vries equation \begin{equation} u_t + \frac{1}{2}u_{xxx}+3|u|^2 u_x=0, \end{equation} with the step-like initial data \begin{equation} u(x,0)=u_0(x)= \begin{cases} 0, & {x \ge 0,}\\ A e^{iBx}, &{x < 0.} \end{cases} \end{equation} It is shown that the step-like initial problem can be described by a matrix Riemann-Hilbert problem. We apply the steepest descent method to obtain different large-time asymptotics in the the Zakharov-Manakov region, a plane wave region and a slow decay region.
