Nonlinear Excitation and State Transition of Multi-Peak Solitons**Supported by the National Natural Science Foundation of China under Grant Nos 11705145 and 11475135, the Guangxi Provincial Education Department Research Project of China under Grant No 2017KY0776, the Scientific Research Program Funded by Shaanxi Provincial Education Department under Grant No 17JK0767, and the Major Basic Research Program of Natural Science of Shaanxi

Abstract

We study the nonlinear excitations in the integrable fifth-order nonlinear Schrödinger equation on a continuous wave background. The excited condition of each localized wave is demonstrated via concise phase diagrams. In particular, the rule of transition between asymmetric and symmetric multi-peak solitons is revealed. It is shown that the initial phase modulation can induce the transition and the transition condition is demonstrated exactly. Interestingly, our result shows that although the multi-peak solitons exhibit structural diversity, both the asymmetric and symmetric states possess an identical asymmetric spectrum structure.