On a novel integrable generalization of the sine-Gordon equation

2009/09/30 by Jonatan Lenells, J. Lenells, A. S. Fokas · 4 citations
Physics and Astronomy · #nlin.PS #nlin.SI

paper · pdf · doi:10.1007/s00332-010-9070-1

24 pages

arxiv created 2010/01/18 · arxiv updated 2015/05/14

Abstract

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.

Cited by

• Nonlocal massive Thirring model and its solutions
• Integrable motion of curves associated with the Fokas-Lenells equation and related spin system
• Bright soliton interactions in the variable coefficient Fokas-Lenells equation, Conservation laws, Modulation instability and Soliton tunneling
• Discretization of the Mikhailov model
• Miura transformation in bidifferential calculus and a vectorial Darboux transformation for the Fokas-Lenells equation

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