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Periodic solitons for the elliptic-elliptic focussing Davey-Stewartson equations
We consider the elliptic-elliptic, focussing Davey-Stewartson equations,
which have an explicit bright line soliton solution. The existence of a family
of periodic solitons, which have the profile of the line soliton in the
longitudinal spatial direction and are periodic in the transverse spatial
direction, is established using dynamical systems arguments. We also show that
the line soliton is linearly unstable with respect to perturbations in the
transverse direction.Comment: arXiv admin note: text overlap with arXiv:1411.247
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