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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:

35Q53 KdV equations (Korteweg-de Vries equations)
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
37-04 Software, source code, etc. for problems pertaining to dynamical systems and ergodic theory

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