An integrable coupled short pulse equation

Abstract

An integrable coupled short pulse (CSP) equation is proposed for the propagation of ultra-short pulses in optical fibers. Based on two sets of bilinear equations to a two-dimensional Toda lattice linked by a Bäcklund transformation, and an appropriate hodograph transformation, the proposed CSP equation is derived. Meanwhile, its N-soliton solutions are given by the Casorati determinant in a parametric form. The properties of one- and two-soliton solutions are investigated in detail. Same as the short pulse equation, the two-soliton solution turns out to be a breather type if the wave numbers are complex conjugate. We also illustrate an example of soliton–breather interaction.