论文标题
反向时空非局部hirota方程的长期渐近造型，具有衰减的初始值问题：没有孤子
Long-time asymptotics for the reverse space-time nonlocal Hirota equation with decaying initial value problem: Without solitons
论文作者
论文摘要
在这项工作中，我们主要考虑反向时空非局部广播方程的库奇问题，而无孤子部门的初始数据迅速衰减。从LAX对开始，我们首先构建反向时空非局部广播方程的基础Riemann-Hilbert问题。此外，使用Deift-Zhou非线性陡峭下降的方法，得出了反向时空非本地Hirota的显式长期渐近物。对于反向时空非局部非局部方程，由于其散射矩阵的对称性与本地hirota方程不同，所以$ \ vartheta（λ_{i}）（i = 0，1）$想成为虚构$ t^{\ frac {\ pm im \ vartheta（λ_{i}）} {2}}} $，然后非局部hirota方程的渐近行为变得不同。
In this work, we mainly consider the Cauchy problem for the reverse space-time nonlocal Hirota equation with the initial data rapidly decaying in the solitonless sector. Start from the Lax pair, we first construct the basis Riemann-Hilbert problem for the reverse space-time nonlocal Hirota equation. Furthermore, using the approach of Deift-Zhou nonlinear steepest descent, the explicit long-time asymptotics for the reverse space-time nonlocal Hirota is derived. For the reverse space-time nonlocal Hirota equation, since the symmetries of its scattering matrix are different with the local Hirota equation, the $\vartheta(λ_{i})(i=0, 1)$ would like to be imaginary, which results in the $δ_{λ_{i}}^{0}$ contains an increasing $t^{\frac{\pm Im\vartheta(λ_{i})}{2}}$, and then the asymptotic behavior for nonlocal Hirota equation becomes differently.
