Toda lattice

The Toda lattice, introduced by Morikazu Toda (1967), is a simple model for a one-dimensional crystal in solid state physics. It is given by a chain of particles with nearest neighbor interaction described by the equations of motion

where ${\displaystyle q(n,t)}$ is the displacement of the ${\displaystyle n}$-th particle from its equilibrium position, and ${\displaystyle p(n,t)}$ is its momentum (mass ${\displaystyle m=1}$).

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