High-low pressure domain wall for the classical Toda lattice

Abstract

We study the classical Toda lattice with domain wall initial conditions, for which left and right half lattice are in thermal equilibrium but with distinct parameters of pressure, mean velocity, and temperature. In the hydrodynamic regime the respective space-time profiles scale ballisticly. The particular case of interest is a jump from low to high pressure at uniform temperature and zero mean velocity. Thereby the scaling function for the average stretch (also free volume) is forced to change sign. By direct inspection, the hydrodynamic equations for the Toda lattice seem to be singular at zero stretch. In our contribution we report on numerical solutions and convincingly establish that nevertheless the self-similar solution exhibits smooth behavior.

arXiv comment15 pages, 2 figures

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• Hydrodynamic equations for the Ablowitz-Ladik discretization of the nonlinear Schroedinger equation
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• Integrable hydrodynamics of Toda chain: case of small systems
• Generalized Hydrodynamics for the Volterra lattice: Ballistic and nonballistic behavior of correlation functions