Breathers and solitons for the coupled nonlinear Schrödinger system in three-spine α-helical protein* *Project supported by the Scientific and Technological Innovation Programs of Higher Education Institution in Shanxi, China (Grant Nos. 2020L0525 and 2019L0782), the National Natural Science Foundation of China (Grant Nos. 11805141 and 12075210), Applied Basic Research Program of Shanxi Province, China (Grant No. 201901D211424),“1331 Project”Key Innovative Research

Abstract

We mainly investigate the variable-coefficient 3-coupled nonlinear Schrödinger (NLS) system, which describes soliton dynamics in the three-spine α-helical protein with inhomogeneous effect. The variable-coefficient NLS equation is transformed into the constant coefficient NLS equation by similarity transformation firstly. The Hirota method is used to solve the constant coefficient NLS equation, and then we get the one- and two-breather solutions of the variable-coefficient NLS equation. The results show that, in the background of plane waves and periodic waves, the breather can be transformed into some forms of combined soliton solutions. The influence of different parameters on the soliton solution and the collision between two solitons are discussed by some graphs in detail. Our results are helpful to study the soliton dynamics in α-helical protein.