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Integrability of a generalized Ito system: the Painlevé test. (English) Zbl 1058.35532
Summary: It is shown that a generalized Ito system of four coupled nonlinear evolution equations passes the Painlevé test for integrability in five distinct cases, two of which were introduced recently by Tam et al. [H. W. Tam, X. B. Hu and D. L. Wang, J. Phys. Soc. Japan 68, 369–379 (1999; Zbl 0944.35007)]. A conjecture is formulated on integrability of a vector generalization of the Ito system.
##### MSC:
 35Q53 KdV-like (Korteweg-de Vries) equations 37K10 Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies