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Title Blow up in coupled parity-time symmetric nonlinear Schr\"odinger equations

Name Dmitry Zezyulin
Country Portugal
Email d.zezyulin@gmail.com
Co-Author(s) J.-P. Dias, M. Figueira, V. V. Konotop
Submit Time 2014-02-20 08:17:41
Special Session 37: Global or/and blowup solutions for nonlinear evolution equations and their applications
We consider the Cauchy problem for a system of two self-focusing nonlinear Schr\"odinger equations with linear and nonlinear coupling. The system is PT symmetric, which means that one of the equations includes the gain term while another equation accounts for the damping. We find sufficient conditions for the finite time blow up in the supercritical case (three or more spatial dimensions). The proof is based on the virial technique arguments. Several other physically relevant particular cases are also discussed and illustrated numerically.