soliton

see text

soliton solutions

lump

exact solutions

rogue waves

equation_74523

soliton_117245

darboux transformation

hirota

Physica D Nonlinear Phenomena

The Darboux transformation (DT) for the coupled complex short pulse (CCSP) equation is constructed through the loop group method. The DT is then utilized to construct various exact solutions including bright-soliton, dark-soliton, breather and rogue wave solutions to the CCSP equation. In case of vanishing boundary condition (VBC), we perform the inverse scattering analysis. Breather and rogue wave solutions are constructed under non-vanishing boundary condition (NVBC). Moreover, we conduct a modulational instability (MI) analysis based on the method of squared eigenfunctions , whose result confirms the condition for the existence of rogue wave solution.

Darboux transformation and solitonic solution to the coupled complex short pulse equation