Vibration of a chain of particles interacting by nonlinear force is investigated. Using a transformation exact solutions to the equation of motion are aimed at. For a special type of interaction potential of the form {aligned} φ(r){=}a/be⁻ᵇʳ+ar+const.,\ (a,b{>}0) {aligned} exact solutions are actually obtained in terms of the Jacobian elliptic functions. It is shown that the system has N “normal modes”. Expansion due to vibration or “thermal expansion” of the chain is also discussed.
No takes yet. Share an insight, caveat, or question.
Morikazu Toda (1967) studied this question.
Synapse has enriched 5 related papers. Consider them for comparative context: