To the complete integrability of long-wave–short-wave interaction equations

Abstract

It is shown that the nonlinear partial differential equations governing the interaction of long and short waves are completely integrable. The methodology used is that of Ablowitz et al. [M. J. Ablowitz, A. Ramani, and A. Segur, Lett. Nuovo Cimento 23, 333 (1980); M. J. Ablowitz, A. Ramani, and H. Segur, J. Math. Phys. 21, 715, 1006 (1980)], though in the last section of our paper the problem also has been discussed in the light of the procedure due to Weiss et al. [J. Weiss, M. Tabor, and G. Carnevale, J. Math. Phys. 24, 522 (1983)] and a Backlünd transformation has been obtained.