On a Painlevé test of a coupled system of Boussinesq and Schrödinger equations

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Abstract
The complete integrability of a new system of nonlinear equations using the technique of Painlevé analysis has been investigated. The system essentially represents a coupling of Boussinesq and Schrödinger equations through nonlinear terms. While the arbitrariness of the expansion coefficients are proved (for a particular branch) in the formalism of Weiss et al. [J. Math. Phys. 24, 522 (1983)], with the reduced ansatz of Kruskal, the consistency of the truncation is proved by a combination of the methodology due to Weiss [J. Math. Phys. 25, 13, 2226 (1984)] and Hirota [Lecture Notes in Physics, Vol. 515 (Springer, Berlin, 1976)]. On the other hand, the Bäcklund transformation for the equations are obtained via the truncation procedure, without the use of Kruskal’s simplification.