| Abstract: |
| In this talk, we study the Cauchy problem for the nonlinear Schrodinger equation with a delta potential. We show that under certain conditions, the supreme norm of the solution tends to infinity in finite time. in order to prove this, we study the associated Lagrangian and Hamiltonian, and derive an estimate of the associated variance. We also derive several conservation laws which a classical solution of the Cauchy problem must also satisfy. |
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