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Matter-wave solitons supported by dissipation
We show how novel types of long-lived self-localized matter waves can be
constructed with Bose-Einstein condensates. The ingredients leading to such
structures are a spatial phase generating a flux of atoms towards the
condensate center and the dissipative mechanism provided by the inelastic
three-body collisions in atomic Bose-Einstein condensates. The outcome is an
striking example of nonlinear structure supported by dissipation
Stabilization of solitons of the multidimensional nonlinear Schrodinger equation: Matter-wave breathers
We demonstrate that stabilization of solitons of the multidimensional
Schrodinger equation with a cubic nonlinearity may be achieved by a suitable
periodic control of the nonlinear term. The effect of this control is to
stabilize the unstable solitary waves which belong to the frontier between
expanding and collapsing solutions and to provide an oscillating solitonic
structure, some sort of breather-type solution. We obtain precise conditions on
the control parameters to achieve the stabilization and compare our results
with accurate numerical simulations of the nonlinear Schrodinger equation.
Because of the application of these ideas to matter waves these solutions are
some sort of matter breathers
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