标题： 渐近可积性及其后果 显示英文标题

标题： Asymptotic integrability and its consequences

摘要： 我们简要回顾了渐近可积性的概念，这意味着沿平滑的大尺度背景波传播短波包的哈密顿方程有一个与初始条件无关的积分。 这种积分的存在导致了一系列重要的结果，除了直接应用于波包传播问题外，还包括窄孤立子运动的哈密顿理论以及由强初始脉冲产生的孤立子参数的广义玻尔-索末菲量子化规则。 我们表明，在具有两个波变量且渐近可积性条件精确满足的情况下，与附加积分相关的力学系统的“量子化”会产生一些典型完全可积方程的Lax对，并这为非线性波物理中完全可积性的起源提供了新的见解。 显示英文摘要

摘要： We give a brief review of the concept of asymptotic integrability, which means that the Hamilton equations for the propagation of short-wavelength packets along a smooth, large-scale background wave have an integral independent of the initial conditions. The existence of such an integral leads to a number of important consequences, which include, besides the direct application to the packets propagation problems, Hamiltonian theory of narrow solitons motion and generalized Bohr-Sommerfeld rule for parameters of solitons produced from an intensive initial pulse. We show that in the case of systems with two wave variables and exact fulfillment of the asymptotic integrability condition, the `quantization' of mechanical systems, associated with the additional integrals, yields the Lax pairs for a number of typical completely integrable equations, and this sheds new light on the origin of the complete integrability in nonlinear wave physics.