Breathers and solitons for the coupled nonlinear Schrödinger system in three-spine α-helical protein*

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.

The non-autonomous generalized perturbed KdV equation: its integrability, infinite conservation laws, multi soliton, high-order breather and hybrid solutions with mixed backgrounds

“…Utilizing proper quadratic function in Hirota's bilinear form we derive multi-soliton, breather, and hybrid solutions. In general, breathers are solutions with periodic local waves in space or time, non mediocre properties caused by the collision reaction of breathers, so breathers are used to explain the modulation instability and the generation of rouge waves [67]. Solitary interaction can be studied using multi-soliton which promotes the multi-soliton as an exciting area in nonlinear fields.…”