Superposition principles associated with the Moutard transformation: an integrable discretization of a (2+1)–dimensional sine–Gordon system
Superposition principles associated with the Moutard transformation: an integrable discretization of a (2+1)–dimensional sine–Gordon system
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DOI：
10.1098/rspa.1997.0015
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发表时间：
1997-02
期刊：
影响因子：
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通讯作者：
J. Nimmo;W. Schief
中科院分区：
文献类型：
--
作者：
J. Nimmo;W. Schief
发现了与 Moutard 变换相关的线性和非线性叠加原理。经过适当的重新解释，它们构成了一个可积的离散非线性系统及其相关的线性系统。进一步表明，在特定形式下，该系统是 (2+1) 维正弦戈登系统的可积离散化。离散非线性系统的解是通过 Moutard 变换的离散模拟来构造的。这些解中包括连续系统的扭结解的离散模拟。
Superposition principles, both linear and nonlinear, associated with the Moutard transformation are found. On suitable reinterpretation, these constitute an integrable discrete nonlinear system and its associated linear system. Further, it is shown that, in a particular form, this system is an integrable discretization of a (2+1)–dimensional sine–Gordon system. Solutions of the discrete nonlinear system are constructed by means of a discrete analogue of the Moutard transformation. Included in these solutions are discrete analogues of the kink solutions of the continuous system.