Geodesic
The dressing chain of discrete symmetries and proliferation of nonlinear equations
Teoretičeskaâ i matematičeskaâ fizika, Tome 115 (1998) no. 2, pp. 199-214

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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 $\pi$-kink type. 
@article{TMF_1998_115_2_a3,
     author = {A. B. Borisov and S. A. Zykov},
     title = {The dressing chain of discrete symmetries and proliferation of nonlinear equations},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {199--214},
     publisher = {mathdoc},
     volume = {115},
     number = {2},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1998_115_2_a3/}
}
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A. B. Borisov; S. A. Zykov. The dressing chain of discrete symmetries and proliferation of nonlinear equations. Teoretičeskaâ i matematičeskaâ fizika, Tome 115 (1998) no. 2, pp. 199-214. http://geodesic.mathdoc.fr/item/TMF_1998_115_2_a3/