论文标题
本尼类型系统的绝热限制
Uniform Adiabatic Limit of Benney type Systems
论文作者
论文摘要
在本文中，我们表明，立方非线性schrödinger方程的溶液是本尼系统解决方案的渐近极限。由于一维Zakharov和1d-Zakharov-Rubenchik系统的解决方案获得了一维转运方程的特征。在拓扑$ l^2（\ mathbb {r}）\ times l^2（\ mathbb {r}）$中达到融合，并在能量空间中近似$ h^1（\ mathbb {r}）\ times limits l^2（\ times l^2（\ times l^2）（\ mathbb {r}）$。在Zakharov系统的情况下，这是可以实现的，而没有条件$ \ partial_t n（x，0）\ in \ dot h^{ - 1}（\ Mathbb {r}）$ for Wave组件，从而改善了先前的结果。
In this paper we show that solutions of the cubic nonlinear Schrödinger equation are asymptotic limit of solutions to the Benney system. Due to the special characteristic of the one-dimensional transport equation same result is obtained for solutions of the one-dimensional Zakharov and 1d-Zakharov-Rubenchik systems. Convergence is reached in the topology $L^2(\mathbb{R})\times L^2(\mathbb{R})$ and with an approximation in the energy space $H^1(\mathbb{R})\times L^2(\mathbb{R})$. In the case of the Zakharov system this is achieved without the condition $\partial_t n(x,0) \in \dot H^{-1}(\mathbb{R})$ for the wave component, improving previous results.
