The modulational instability of the nonlinear Schrödinger (NLS) equation is examined in the case with a quadratic external potential. This study is motivated by recent experimental results in the context of matter waves in Bose-Einstein condensates (BECs). The theoretical analysis invokes a lens-type transformation that converts the Gross-Pitaevskii into a modified NLS equation without explicit spatial dependence. This analysis suggests the particular interest of a specific time-varying potential $\left[\sim {(t+t}^{*}{)}^{-2}\right].$ We examine both this potential, as well as the time-independent one numerically and conclude by suggesting experiments for the production of solitonic wave trains in BECs.

• Received 27 December 2002

DOI:https://doi.org/10.1103/PhysRevA.67.063610