论文标题
在Kuznetsov-Ma呼吸器的大订单上
On the large-order asymtptics of Kuznetsov-Ma breathers
论文作者
论文摘要
我们研究了远场政权中非线性schrödinger方程的kuznetsov-ma呼吸的大渐近分析。在Darboux Transformation的帮助下，我们首先为高阶Kuznetsov-Ma呼吸器提供了相应的Riemann-Hilbert代表。在远场极限下，在时空平面上有五个渐近区域，呼吸器的行为不同，两国属区域，代数 - 赛季区域和三个不同的零属区域。借助Deift-Zhou非线性最陡的方法，我们给出了每个区域的主要顺序项，并通过数值验证精确溶液与渐近溶液之间的一致性。与先前关于流氓波和孤子大型渐近分析的研究相比，我们发现了一个新型的两种渐近区域，这进一步丰富了大型动力学的研究。
We study the large-order asymptotics for the Kuznetsov-Ma breather of the nonlinear Schrödinger equation in the far-field regime. With the aid of Darboux transformation, we first derive the corresponding Riemann-Hilbert representation for the high-order Kuznetsov-Ma breathers. Under the far-field limit, there are five asymptotical regions in the space-time plane where the breathers behave differently, the genus-two region, the algebraic-decay region, and three distinct genus-zero regions. With the aid of the Deift-Zhou nonlinear steepest decent method, we give the leading order term for each region and verify the consistency between the exact solution and the asymptotic solution numerically. Compared to the previous studies about the large-order asymptotic analysis of rogue waves and solitons, we find a novel genus-two asymptotic region, which further enriches the research of large-order dynamics.
