论文标题
在四阶非线性schrödinger方程中的多脉冲孤立波
Multi-pulse solitary waves in a fourth-order nonlinear Schrödinger equation
论文作者
论文摘要
在目前的工作中，我们考虑了多脉冲孤立波解决方程的多脉冲孤立波解决方程的存在和光谱稳定性，并具有第四阶和二阶分散项。我们首先根据分散术语的系数存在一个单孤波解的标准，然后证明存在一个离散的多脉冲溶液家族，其特征在于各个脉冲之间的距离。然后，我们将这些多脉冲的光谱稳定性问题减少到计算矩阵的决定因素，该基质是领先的，即导致对角线。在一个可以通过数值验证的其他假设下，我们表明所有多脉冲都在光谱上不稳定。对于双重脉冲，提出了与我们的分析结果非常吻合的数值计算。
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.
