论文标题
准简单色散电击波和从非线性脉冲演变而来的孤子数量的理论
Theory of quasi-simple dispersive shock waves and number of solitons evolved from a nonlinear pulse
论文作者
论文摘要
在简单波的波浪破裂后产生的分散冲击波的边缘运动理论得以发展。结果表明，这种运动服从汉密尔顿力学，与类似HOPF的方程式相辅相成，用于与边缘波数据包或边缘孤子相互作用的背景流的演变。关于小振幅和孤子边缘方程之间存在某种对称性的猜想。如果局部简单波脉冲通过静止介质传播，则该理论为最终从这种脉冲产生的孤子数量的渐近公式提供了一种新方法。
The theory of motion of edges of dispersive shock waves generated after wave breaking of simple waves is developed. It is shown that this motion obeys Hamiltonian mechanics complemented by a Hopf-like equation for evolution of the background flow that interacts with edge wave packets or edge solitons. A conjecture about existence of a certain symmetry between equations for the small-amplitude and soliton edges is formulated. In case of localized simple wave pulses propagating through a quiescent medium this theory provided a new approach to derivation of an asymptotic formula for the number of solitons produced eventually from such a pulse.
