International Journal of Mathematics and Mathematical Sciences
Volume 9 (1986), Issue 3, Pages 541-544

On the complete integrability of an equation having solitons but not known to have a Lax pair

A. Roychowdhury and G. Mahato

High Energy Physics Division, Jadavpur University, Calcutta 700032, India

Received 19 March 1985

Copyright © 1986 A. Roychowdhury and G. Mahato. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


It is usually assumed that a system having N-soliton solutions is completely integrable. Here we have analyzed a set of equations occuring in case of capillary gravity waves. Though the system under discussion has N-soliton solutions, it has yet to be shown that the system is completely integrable. No Lax pair is known for the system. Here we show that the system is not completely integrable in the sense of Ablowitz et al.