标题： 暗孤子在大尺度背景上的传播 显示英文标题

标题： Propagation of dark solitons of DNLS equation along a large-scale background

摘要： 我们通过基于施加该动力学必须为哈密顿的条件的方法，研究DNLS方程理论中暗孤子的动力学。 将此条件与斯托克斯的评论相结合，即谐波线性波和小振幅孤子尾部的关系满足相同的线性化方程，因此相应的解可以通过将包的波数$k$替换为$i\kappa$来相互转换，$\kappa$是孤子的逆半宽度，我们找到孤子运动的哈密顿量和正则动量。 哈密顿方程被简化为牛顿方程，其某些典型情况的解与DNLS方程的精确数值解进行比较。 显示英文摘要

摘要： We study dynamics of dark solitons in the theory of the DNLS equation by the method based on imposing the condition that this dynamics must be Hamiltonian. Combining this condition with Stokes' remark that relationships for harmonic linear waves and small-amplitude soliton tails satisfy the same linearized equations, so the corresponding solutions can be converted one into the other by replacement of the packet's wave number $k$ by $i\kappa$, $\kappa$ being the soliton's inverse half-width, we find the Hamiltonian and the canonical momentum of the soliton's motion. The Hamilton equations are reduced to the Newton equation whose solutions for some typical situations are compared with exact numerical solutions of the DNLS equation.