论文标题
具有非本地衍生物的二维非线性Schrödinger方程的呼吸溶液
Breather Solutions to a Two-dimensional Nonlinear Schrödinger Equation with Non-local Derivatives
论文作者
论文摘要
我们考虑在二维周期域中具有非本地衍生物的非线性schrödinger方程。对于某些衍生物的顺序，我们发现在低非线性水平下占主导地位的新型呼吸溶液。随着非线性的增加，呼吸器崩溃，让位于湍流（或雷利 - 吉恩）光谱。发现与呼吸溶液相关的相位轨迹与线性系统的相关轨迹接近，从而揭示了呼吸溶液与Kolmogorov-Arnold-Moser（KAM）理论之间的联系。
We consider the nonlinear Schrödinger equation with non-local derivatives in a two-dimensional periodic domain. For certain orders of derivatives, we find a new type of breather solution dominating the field evolution at low nonlinearity levels. With the increase of nonlinearity, the breathers break down, giving way to wave turbulence (or Rayleigh-Jeans) spectra. Phase-space trajectories associated with the breather solutions are found to be close to that of the linear system, revealing a connection between the breather solution and Kolmogorov-Arnold-Moser (KAM) theory.
