Long-time asymptotics of the focusing Kundu-Eckhaus equation with nonzero boundary conditions
Long-time asymptotics of the focusing Kundu-Eckhaus equation with nonzero boundary conditions
复制标题
非零边界条件下聚焦 Kundu-Eckhaus 方程的长时渐近
DOI：
10.1016/j.jde.2018.10.053
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发表时间：
2019
影响因子：
2.4
通讯作者：
Wang Xiaoli
中科院分区：
文献类型：
--
作者：
Wang Deng-Shan;Guo Boling;Wang Xiaoli
用Deift和周的非线性最速下降法研究了具有无穷远非零边界条件的聚焦Kundu-Eck haus方程的长时间渐近性。在时空平面上发现了三个渐近扇区：平面波扇区I、平面波扇区II和一个带有调制的单相椭圆波的中间扇区。通过将相应的Riemann-Hilbert问题依次转化为可解的模型问题，得到了这三个扇区的渐近解。此外，还引入了一种含时函数机制来消除调制单相椭圆波扇区中跳跃矩阵的指数增长。最后，研究了调制不稳定性，揭示了中心区存在调制椭圆波的判据。
The long-time asymptotics of the focusing Kundu–Eckhaus equation with nonzero boundary conditions at infinity is investigated by the nonlinear steepest descent method of Deift and Zhou. Three asymptotic sectors in space–time plane are found: the plane wave sector I, plane wave sector II and an intermediate sector with a modulated one-phase elliptic wave. The asymptotic solutions of the three sectors are proposed by successively deforming the corresponding Riemann–Hilbert problems to solvable model problems. Moreover, a time-dependentg-function mechanism is introduced to remove the exponential growths of the jump matrices in the modulated one-phase elliptic wave sector. Finally, the modulational instability is studied to reveal the criterion for the existence of modulated elliptic waves in the central region.