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The dressing chain of discrete symmetries and proliferation of nonlinear equations

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Abstract

In the examples of sine-Gordon and Korteweg-de Vries (KdV) equations, we propose a direct method for using dressing chains (discrete symmetries) to proliferate integrable equations. We give a recurrent procedure (with a finite number of steps in general) that allows the step-by-step production of an integrable system and its L-A pair from the known L-A pair of an integrable equation. Using this algorithm, we reproduce a number of known results for integrable systems of the KdV type. We also find a new integrable equation of the sine-Gordon series and investigate its simplest soliton solution of the double π-kink type.

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Authors and Affiliations

  1. Institute for the Physics of Metals. Urals Branch, Russian Academy of Sciences, Ekaterinburg, Russia

    A. B. Borisov & S. A. Zykov

Authors
  1. A. B. Borisov
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  2. S. A. Zykov
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Translated from Teoreticheskaya i Matematicheskaya Fizika. Vol. 115. No. 2. pp. 199–214. May. 1998.

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Borisov, A.B., Zykov, S.A. The dressing chain of discrete symmetries and proliferation of nonlinear equations. Theor Math Phys 115, 530–541 (1998). https://doi.org/10.1007/BF02575453

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