Linear Instability of Breathers for the Focusing Nonlinear Schrödinger Equation
Linear Instability of Breathers for the Focusing Nonlinear Schrödinger Equation
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DOI：
10.1007/s00332-022-09819-4
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发表时间：
2021-12
影响因子：
3
通讯作者：
M. Haragus;D. Pelinovsky
中科院分区：
文献类型：
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作者：
M. Haragus;D. Pelinovsky
借助可积系统理论的工具，讨论了聚焦非线性薛定谔方程的Kuznetsov-Ma呼吸子和Akhmediev呼吸子的线性不稳定性.我们利用达布变换同时构造了呼吸子和与呼吸子相关的Lax系统的精确解。我们得到一个完整的描述的拉克斯光谱的两个呼吸，包括多重的本征值。线性化NLS方程的解，然后从Lax系统的本征函数和广义本征函数获得。虽然我们不试图证明本征函数的完备性，但我们的目标是确定Lax系统在适当的函数空间中产生的线性化NLS方程的整组解。
Relying upon tools from the theory of integrable systems, we discuss the linear instability of the Kuznetsov–Ma breathers and the Akhmediev breathers of the focusing nonlinear Schrödinger equation. We use the Darboux transformation to construct simultaneously the breathers and the exact solutions of the Lax system associated with the breathers. We obtain a full description of the Lax spectra for the two breathers, including multiplicities of eigenvalues. Solutions of the linearized NLS equations are then obtained from the eigenfunctions and generalized eigenfunctions of the Lax system. While we do not attempt to prove completeness of eigenfunctions, we aim to determine the entire set of solutions of the linearized NLS equations generated by the Lax system in appropriate function spaces.