Breathers, rogue waves, and interaction solutions for the variable coefficient Kundu-nonlinear Schrödinger equation

With the inhomogeneity of optical fiber media taken into account, under investigation in this paper is the variable coefficient Kundu-nonlinear Schrödinger equation, which describes the pulses propagation in optical fibers. Based on Lax pair, the Nth-order Darboux transformation is constructed. Depending on plane wave solution, the first- and second-order breather solutions are derived and the interactions between breathers are graphically analyzed. The Kuznetsov–Ma breather, Akhmediev breather, and spatial-temporal breather have been obtained. Moreover, the first-, second-, and third-order rogue wave solutions have been constructed. The usual rogue waves and first- and second-order line rogue waves are observed. The weak and strong interactions between the first-, second-order rogue waves, and spatial-temporal period breather are studied. Furthermore, variable coefficient δ ( t ) causes rogue waves to produce some interesting evolutionary phenomena, which have been systematically analyzed. In addition, the influences of parameters for the properties of solutions are discussed.