Consider an infinite linear chain of rotors each described by a phase variable n , with

Consider an infinite linear chain of rotors each described by a phase variable θ_n, with n ∈ Z. The rotors are coupled to their neighbours and their equation of motion is given by

Make use of the continuum approximation given by

Assume that the initial configuration of the chain is given by θ(x,0) = ϕ(x).

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den = n + 1 (On+1 - On) + y (On-1 - On). dt