On a novel integrable generalization of the sine-Gordon equation
J. Lenells, A. S. Fokas
TL;DR
This paper introduces a new integrable generalization of the sine-Gordon equation, deriving its Lax pair, solving the initial value problem, analyzing solitons and traveling waves, and establishing its relation to the classical sG equation.
Contribution
It presents a novel integrable generalization of the sine-Gordon equation with explicit Lax pair, solution methods, and analysis of solitons and wave solutions.
Findings
Derived a Lax pair for the generalized sG equation
Solved the initial value problem on the line
Analyzed soliton and traveling-wave solutions
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.
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