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引用次数: 0
摘要
阿布罗维茨-拉迪克(AL)链是非线性薛定谔方程的可积分离散化版本。我们报告了一个新颖的底层哈密顿粒子系统,其性质类似于已知的经典托达链和具有成对相互作用的卡洛吉罗流体。施加的边界条件使得粒子在遥远的过去和未来都具有恒定的速度。我们建立了 AL 链的多粒子散射,并获得了一般可积分多体系统的已知性质。对于链的特定选择,真实的初始数据在时间过程中保持真实。然后,渐进地,粒子成对运动,其大小与速度有关,散射位移受融合规则支配。
Particle scattering and fusion for the Ablowitz–Ladik chain
The Ablowitz–Ladik (AL) chain is an integrable discretized version of the nonlinear Schrödinger equation. We report on a novel underlying Hamiltonian particle system with properties similar to the ones known for the classical Toda chain and Calogero fluid with pair interaction. Boundary conditions are imposed such that, both in the distant past and future, particles have a constant velocity. We establish the many-particle scattering for the AL chain and obtain properties known for generic integrable many-body systems. For a specific choice of the chain, real initial data remain real in the course of time. Then, asymptotically, particles move in pairs with a velocity-dependent size and scattering shifts are governed by the fusion rule.
期刊介绍:
Publishing 50 issues a year, Journal of Physics A: Mathematical and Theoretical is a major journal of theoretical physics reporting research on the mathematical structures that describe fundamental processes of the physical world and on the analytical, computational and numerical methods for exploring these structures.