论文标题
多相调制理论的有效性证明
A proof of validity for multiphase Whitham modulation theory
论文作者
论文摘要
事实证明，作为多相WHITHAM调制方程的解决方案获得的近似值保持在自然时间尺度上接近原始方程的解决方案。为起点选择的非线性波方程类别是耦合的非线性schrödinger方程。这些方程通常不可集中，但是它们具有显式的多相波动素家族，它们会产生可能是椭圆形，双曲线或混合类型的多相hitham方程。由于类型的变化，该功能空间设置基于Gevrey空间，在复杂平面的带中具有初始数据分析。在这些空间中，证明了Cauchy-Kowalevskaya的存在和独特定理。在该定理和对Whitham理论的高阶近似基础上，耦合的非线性schrödinger方程和多相调制方程的溶液进行了严格的比较。
It is proved that approximations which are obtained as solutions of the multiphase Whitham modulation equations stay close to solutions of the original equation on a natural time scale. The class of nonlinear wave equations chosen for the starting point is coupled nonlinear Schrödinger equations. These equations are not in general integrable, but they have an explicit family of multiphase wavetrains that generate multiphase Whitham equations which may be elliptic,hyperbolic, or of mixed type. Due to the change of type, the function space setup is based on Gevrey spaces with initial data analytic in a strip in the complex plane. In these spaces a Cauchy- Kowalevskaya-like existence and uniqueness theorem is proved. Building on this theorem and higher-order approximations to Whitham theory, a rigorous comparison of solutions, of the coupled nonlinear Schrödinger equations and the multiphase Whitham modulation equations, is obtained.
