Supercritical blowup in coupled parity-time-symmetric nonlinear Schrödinger equations

Abstract

We prove finite time supercritical blowup in a parity-time-symmetric system of the two coupled nonlinear Schrödinger (NLS) equations. One of the equations contains gain and the other one contains dissipation such that strengths of the gain and dissipation are equal. We address two cases: in the first model all nonlinear coefficients (i.e. the ones describing self-action and non-linear coupling) correspond to attractive (focusing) nonlinearities, and in the second case the NLS equation with gain has attractive nonlinearity while the NLS equation with dissipation has repulsive (defocusing) nonlinearity and the nonlinear coupling is repulsive, as well. The proofs are based on the virial technique arguments. Several particular cases are also illustrated numerically.

17 pages, 4 figures; accepted for Studies In Applied Mathematics

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• Constructing Solvable Models of Vector Non-linear Schrodinger Equation with Balanced Loss and Gain via Non-unitary transformation
• Classical Hamiltonian Systems with Balanced loss and gain