On a novel integrable generalization of the sine-Gordon equation

Details On a novel integrable generalization of the sine-Gordon equation On a novel integrable generalization of the sine-Gordon equation

2009-09-14

arxiv.org/abs/0909.2590v2

Nonlinear Sciences

Exactly Solvable and Integrable Systems

24 pages

Scientific paper

We consider an integrable generalization of the sine-Gordon (sG) equation that was earlier derived by one of the authors using bi-Hamiltonian methods. This equation is related to the sG equation in the same way that the Camassa-Holm equation is related to the KdV equation. In this paper we: (a) Derive a Lax pair. (b) Use the Lax pair to solve the initial value problem on the line. (c) Analyze solitons. (d) Show that the generalized sG and sG equations are related by a Liouville transformation. (e) Derive conservation laws. (f) Analyze traveling-wave solutions.

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