Tam, Hon-Wah; Hu, Xing-Biao; Wang, Dao-Liu Two integrable coupled nonlinear systems. (English) Zbl 0944.35077 J. Phys. Soc. Japan 68, No. 2, 369-379 (1999). 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. Cited in 3 Documents 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 Keywords:coupled KdV equation; coupled Ito system; reduction; BKP hierarchy; Bäcklund transformation; soliton solution Software:Mathematica PDFBibTeX XMLCite \textit{H.-W. Tam} et al., J. Phys. Soc. Japan 68, No. 2, 369--379 (1999; Zbl 0944.35077) Full Text: DOI