Global Existence of Solutions to Coupled 𝒫𝒯-Symmetric Nonlinear Schrödinger Equations

We study a system of two coupled nonlinear Schrödinger equations, where one equation includes gain and the other one includes losses. Strengths of the gain and the loss are equal, i.e., the resulting system is parity-time (𝒫𝒯$$\mathcal {PT}$$) symmetric. The model includes both linear and nonlinear couplings, such that when all nonlinear coefficients are equal, the system represents the 𝒫𝒯$$\mathcal {PT}$$-generalization of the Manakov model. …