Physics – Condensed Matter – Soft Condensed Matter
Scientific paper
2004-09-06
Physics
Condensed Matter
Soft Condensed Matter
6 pages, 4 figures, Phys. Rev. A (in press)
Scientific paper
10.1103/PhysRevA.70.063605
In this paper, an exact unitary transformation is examined that allows for the construction of solutions of coupled nonlinear Schr{\"o}dinger equations with additional linear field coupling, from solutions of the problem where this linear coupling is absent. The most general case where the transformation is applicable is identified. We then focus on the most important special case, namely the well-known Manakov system, which is known to be relevant for applications in Bose-Einstein condensates consisting of different hyperfine states of $^{87}$Rb. In essence, the transformation constitutes a distributed, nonlinear as well as multi-component generalization of the Rabi oscillations between two-level atomic systems. It is used here to derive a host of periodic and quasi-periodic solutions including temporally oscillating domain walls and spiral waves.
Deconinck Bernard
Frantzeskakis Dimitri J.
Kevrekidis Panagiotis G.
Nistazakis Hector E.
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