Higher-order mixed solution and breather solution on a periodic background for the Kundu equation

In this paper, we use the generalized Darboux transformation (GDT) method and the Taylor expansion to construct solutions for the Kundu equation including the multiple breather solution on a periodic background and the mixed solutions of multiple soliton and multiple breather solution. Starting from the Lax pair under the framework of Kaup- Newell (KN) system, we obtain an odd-fold Darboux transformation. Then by means of the Taylor expansion, the odd-fold GDT is obtained in the form of determinants. By selecting different parameters in the determinants, we find various solutions. Modulation instability (MI) for the Kundu equation is also studied as a small aspect. (c) 2023 Elsevier B.V. All rights reserved.