Generalized Darboux transformation and Nth order rogue wave solution of a general coupled nonlinear Schrödinger equations

• Generalized Darboux transformation of a general coupled nonlinear Schrödinger (GCNLS) system is constructed.
• Recursive formula and determinant representation of Nth order rogue wave solution of GCNLS system is presented.
• The explicit forms of first, second and third-order rogue wave solutions to the GCNLS system are given.

We construct a generalized Darboux transformation (GDT) of a general coupled nonlinear Schrödinger (GCNLS) system. Using GDT method we derive a recursive formula and present determinant representations for Nth order rogue wave solution of this system. Using these representations we derive first, second and third order rogue wave solutions with certain free parameters. By varying these free parameters we demonstrate the formation of triplet, triangle and hexagonal patterns of rogue waves.