Gene

Quantum mechanics

Transformation (genetics)

Rogue wave

Mathematical physics

Nonlinear Schrödinger equation

Biochemistry

Breather

Physics

Nonlinear system

Mathematics

Mathematical analysis

Chemistry

Schrödinger equation

Applied Mathematics and Computation

An extended generalized Darboux transformation method is proposed to construct the hybrid rogue wave and breather solutions for a classical nonlinear Schrödinger equation. Three types of hybrid wave solutions are obtained: (i) the hybrid first-order rogue wave and breather; (ii) the hybrid second-order rogue wave and first-order breather; (iii) the hybrid first-order rogue wave and second-order breather. These solutions are novel and can be used to investigate the dynamical characteristic of the hybrid rogue waves and breathers. The control and interaction based on the parameters of the hybrid wave solution are graphically demonstrated. An exact link is established between the hybrid solutions and the rogue wave solutions via setting the parameter at special value.

Extended generalized Darboux transformation to hybrid rogue wave and breather solutions for a nonlinear Schrödinger equation