New classes of solutions in the Coupled PT Symmetric Nonlocal Nonlinear Schrodinger Equations with Four Wave Mixing (1804.04914v1)

Abstract: We investigate generalized nonlocal coupled nonlinear Schroedinger equation containing Self-Phase Modulation, Cross-Phase Modulation and Four-Wave Mixing involving nonlocal interaction. By means of Darboux transformation, we obtained a family of exact breathers and solitons including the Peregrine soliton, Kuznetsov-Ma breather, Akhmediev breather along with all kinds of soliton-soliton and breather-soliton interactions. We analyze and emphasize the impact of the four-wave mixing on the nature and interaction of the solutions. We found that the presence of Four-Wave Mixing converts a two-soliton solution into an Akhmediev breather. In particular, the inclusion of Four-Wave Mixing results in the generation of a new solution which is spatially and temporally periodic called "Soliton (Breather) lattice".