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Zbl 0944.35077
Tam, Hon-Wah; Hu, Xing-Biao; Wang, Dao-Liu
Two integrable coupled nonlinear systems. (English)
[J] J. Phys. Soc. Japan 68, No.2, 369-379 (1999). ISSN 0031-9015; ISSN 1347-4073/e

Summary: Motivated by Hirota and Satsuma's results on their coupled KdV equation, two integrable coupled nonlinear systems are considered. One of them is a coupled Ito system. It is shown that the coupled Ito system is a special case of the $(6,2)$-reduction of the two component BKP hierarchy while the other coupled system can be obtained from the $(5,1)$-reduction of the two component BKP hierarchy. By using MATHEMATICA, we obtain the 3- and 4-soliton solutions of the coupled Ito system. In addition, starting from bilinear equations of the other coupled system, a Bäcklund transformation is found and nonlinear superposition formulae are established. Soliton solutions and rational solutions are also derived from these results.

MSC 2000:: *35Q53 KdV-like equations
37K10 Completely integrable systems etc.
37-04 Machine computation, programs (Dynamical systems and ergodic theory)

Keywords: coupled KdV equation; coupled Ito system; reduction; BKP hierarchy; Bäcklund transformation; soliton solution

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