Riemann–Hilbert approach, dark solitons and double‐pole solutions for Lakshmanan–Porsezian–Daniel equation in an optical fiber, a ferromagnetic spin or a protein

Author:

Chen Su‐Su12ORCID,Tian Bo1,Tian He‐Yuan1,Hu Cong‐Cong1

Affiliation:

1. State Key Laboratory of Information Photonics and Optical Communications, and School of Science Beijing University of Posts and Telecommunications Beijing China

2. School of Mathematics and Statistics Yunnan University Kunming China

Abstract

AbstractInverse scattering transform for the defocusing Lakshmanan–Porsezian–Daniel equation with nonzero boundary condition is constructed via the Riemann–Hilbert approach. Since poles of the associated reflection coefficient are simple, ‐dark soliton solutions corresponding to simple poles are constructed. For ‐dark soliton solutions, results show that the soliton amplitude and width are not affected by the strength of the higher‐order linear and nonlinear effects , but soliton velocity has a linear correlation with ; the interactions between the two‐dark solitons and among the three‐dark solitons are elastic and experience phase and position shifts. Besides, asymptotic analysis of the double‐pole solutions for the focusing Lakshmanan–Porsezian–Daniel equation with nonzero boundary condition is presented. Different from ‐dark soliton solutions which locate in the straight lines and experience position shift after the interaction, the double‐pole solutions diverge from each other logarithmically and experience no position shift after the interaction.

Funder

National Natural Science Foundation of China

Fundamental Research Funds for the Central Universities

Publisher

Wiley

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