标题： 非局部导数NLS方程中的行进周期波和呼吸子 显示英文标题

标题： Traveling periodic waves and breathers in the nonlocal derivative NLS equation

摘要： 非局部导数NLS（非线性薛定谔）方程描述了分层流体中波的调制以及Calogero--Moser--Sutherland粒子系统的连续极限。 对于该方程的非聚焦版本，我们证明了非零常数背景在衰减和周期扰动下的线性稳定性以及在周期扰动下的非线性稳定性。 对于该方程的聚焦版本，我们在一些限制条件下证明了非零常数背景的线性和非线性稳定性。 对于两种版本，我们通过Hirota双线性方法表征了行波周期波解，分别在非零和零背景上。 对于每一类行波周期波，我们构造了描述在稳定背景上移动的孤立波的呼吸子族。 一种具有$N$个孤立波在行波周期波背景上传播的一般呼吸子解以闭合行列式形式推导得出。 显示英文摘要

摘要： A nonlocal derivative NLS (nonlinear Schr\"{o}dinger) equation describes modulations of waves in a stratified fluid and a continuous limit of the Calogero--Moser--Sutherland system of particles. For the defocusing version of this equation, we prove the linear stability of the nonzero constant background for decaying and periodic perturbations and the nonlinear stability for periodic perturbations. For the focusing version of this equation, we prove linear and nonlinear stability of the nonzero constant background under some restrictions. For both versions, we characterize the traveling periodic wave solutions by using Hirota's bilinear method, both on the nonzero and zero backgrounds. For each family of traveling periodic waves, we construct families of breathers which describe solitary waves moving across the stable background. A general breather solution with $N$ solitary waves propagating on the traveling periodic wave background is derived in a closed determinant form.