Explicit multiple solitons of the mixed Chen–Lee–Liu equation derived from the Riemann–Hilbert approach

Abstract

The Riemann–Hilbert approach is applied to the mixed Chen–Lee–Liu equation. The corresponding Jost solutions are found, the analytic, asymptotic and symmetric properties of Jost solutions are studied, and a modified Riemann–Hilbert problem is constructed that satisfies the normalization condition. The formulas for multiple solitons related to the simple poles of the Riemann–Hilbert problem are given in determinant form. According to the Cauchy–Binet formula, the formulas for multiple solitons are given explicitly. Based on these explicit formulas, the first- and second-order solitons are obtained, and the multiple-soliton collisions are verified to be elastic.