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Two integrable coupled nonlinear systems. (English) Zbl 0944.35077
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:
35Q53KdV-like (Korteweg-de Vries) equations
37K10Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies
37-04Machine computation, programs (Dynamical systems and ergodic theory)
Software:
Mathematica