### AIMS Mathematics

2017, Issue 1: 195-206. doi: 10.3934/Math.2017.1.195
Research article

# Critical blowup in coupled Parity-Time-symmetric nonlinear Schrödinger equations

• Received: 10 February 2017 Accepted: 14 February 2017 Published: 27 March 2017
• In this article, we obtain suffcient conditions to obtain finite time blowup in a system of two coupled nonlinear Schrödinger (NLS) equations in the critical case. This system mainly considered here in dimension 2, couples one equation including gain and the other one including losses, constituting a generalization of the model of pulse propagation in birefringent optical fibers. In the spirit of the seminal work of Glassey, the proofs used the virial technique arguments.

Citation: Edès Destyl, Silvere Paul Nuiro, Pascal Poullet. Critical blowup in coupled Parity-Time-symmetric nonlinear Schrödinger equations[J]. AIMS Mathematics, 2017, 2(1): 195-206. doi: 10.3934/Math.2017.1.195

### Related Papers:

• In this article, we obtain suffcient conditions to obtain finite time blowup in a system of two coupled nonlinear Schrödinger (NLS) equations in the critical case. This system mainly considered here in dimension 2, couples one equation including gain and the other one including losses, constituting a generalization of the model of pulse propagation in birefringent optical fibers. In the spirit of the seminal work of Glassey, the proofs used the virial technique arguments.

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