On a novel integrable generalization of the sine-Gordon equation
On a novel integrable generalization of the sine-Gordon equation
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DOI：
10.1063/1.3272086
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发表时间：
2010-02
影响因子：
1.3
通讯作者：
J. Lenells;A. Fokas
中科院分区：
文献类型：
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作者：
J. Lenells;A. Fokas
我们考虑了早先由作者之一用双哈密顿方法导出的sin - gordon （sG）方程的可积推广。这个方程与sG方程的关系就像Camassa-Holm方程与Korteweg-de Vries方程的关系一样。本文(a)导出了Lax对，(b)利用Lax对求解了直线上的初值问题，(c)分析了孤子，(d)证明了广义sG方程和sG方程是由Liouville变换联系起来的，(e)导出了守恒定律，(f)分析了行波解。
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 Korteweg–de Vries 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, and (f) analyze traveling-wave solutions.