Toda Lattice

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In 1967, Morikazu Toda introduced a simple model for a one-dimensional crystal, known as the Toda lattice, consisting of a chain of particles with exponential nearest-neighbor interactions.

Contributed by: Enrique Zeleny (May 2013)
Open content licensed under CC BY-NC-SA



From the Hamiltonian


we can derive the equations of motion



where represents the displacement of the particle from its equilibrium position and is its momentum. The Toda lattice shows solitonic behavior that makes it a significant example in the theory of integrable systems.


[1] G. Teschl, "Almost Everything You Always Wanted to Know about the Toda Equation," Jahresbericht der Deutschen Mathematiker-Vereinigung, 103(4), 2001 pp. 149–162.

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