Rational solutions to the cylindrical nonlinear Schrödinger equation: Rogue waves, breathers, and Jacobi breathers solutions

The exact cylindrical rational solutions including cylindrical rogue waves (RWs), cylindrical Kuznetsov–Ma breathers (KMBs), cylindrical Akhmediev breathers (ABs), and cylindrical Jacobi breathers solutions to the cylindrical nonlinear Schrödinger equation (CNLSE) are derived. Also, the criteria for the cylindrical modulational instability and the existence of cylindrical rational solutions are discussed. The obtained solutions could be used for studying the characteristic behavior of all time evolution cylindrical modulated envelope structures in different branches of science such as oceans, seas, water tanks, optical fiber, Veins, capillary tubes, plasma physics, and so on.