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Two Integrable Coupled Nonlinear Systems

Hon-Wah Tam
Xing-Biao Hu
D. L. Wang
Journal / Anthology

Journal of the Physical Society of Japan
Year: 1999
Volume: 68
Issue: 2
Page range: 369-379

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.

*Mathematics > Calculus and Analysis > Differential Equations