Complex short pulse and coupled complex short pulse equations

In the present paper, we propose a complex short pulse equation and a coupled complex short equation to describe ultra-short pulse propagation in optical fibers. They are integrable due to the existence of Lax pairs and infinite number of conservation laws. Furthermore, we find their multi-soliton solutions in terms of pfaffians by virtue of Hirota's bilinear method. One- and two-soliton solutions are investigated in details, showing favorable properties in modeling ultra-short pulses with a few optical cycles. Especially, same as the coupled nonlinear Schrödinger equation, there is an interesting phenomenon of energy redistribution in soliton interactions. It is expected that, for the ultra-short pulses, the complex and coupled complex short pulses equation will play the same roles as the nonlinear Schrödinger equation and coupled nonlinear Schrödinger equation.