Article ID Journal Published Year Pages File Type
1895340 Physica D: Nonlinear Phenomena 2015 11 Pages PDF
Abstract

In this study, we consider a natural integrable generalization of the defocusing cubic nonlinear Schrödinger equation to two dimensions and we classify the admissible boundary conditions. In particular, we determine whether the classical physical observables are conserved: mass, momentum, and Hamiltonian. We find that this is the case when a certain integral (the mass constraint) vanishes. The vanishing of the mass constraint, and thus the existence of conserved quantities, is contingent on the boundary conditions adopted. In particular, under decaying boundary conditions, the Hamiltonian is not necessarily conserved.

Related Topics
Physical Sciences and Engineering Mathematics Applied Mathematics
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