四阶非线性薛定谔方程中的多脉冲孤立波
Multi-pulse solitary waves in a fourth-order nonlinear Schrödinger equation
摘要：
本文研究了一类具有四阶和二阶色散项的非线性薛定谔方程的多脉冲孤立波解的存在性和谱稳定性。我们首先给出了一个单孤立波解存在的色散项的系数，然后表明，一个离散的家庭的多脉冲解的存在，其特征在于由单个脉冲之间的距离。然后，我们减少了这些多脉冲的谱稳定性问题，以计算矩阵的行列式，这是领先的顺序，块对角。在一个附加的假设下，我们证明了所有的多脉冲都是光谱不稳定的。对于双脉冲，数值计算与我们的分析结果是一致的。
英文摘要：
In the present work, we consider the existence and spectral stability of multi-pulse solitary wave solutions to a nonlinear Schrödinger equation with both fourth and second order dispersion terms. We first give a criterion for the existence of a single solitary wave solution in terms of the coefficients of the dispersion terms, and then show that a discrete family of multi-pulse solutions exists which is characterized by the distances between the individual pulses. We then reduce the spectral stability problem for these multi-pulses to computing the determinant of a matrix which is, to leading order, block diagonal. Under an additional assumption, which can be verified numerically, we show that all multi-pulses are spectrally unstable. For double pulses, numerical computations are presented which are in good agreement with our analytical results.
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