Bose-Einstein condensates and spectral properties of      multicomponent nonlinear Schrödinger equations

Vladimir S. Gerdjikov

doi:10.3934/dcdss.2011.4.1181

Article Contents

2011, Volume 4, Issue 5: 1181-1197. Doi: 10.3934/dcdss.2011.4.1181

This issue Previous Article Complex spatiotemporal behavior in a chain of one-way nonlinearly coupled elements Next Article Multiple dark solitons in Bose-Einstein condensates at finite temperatures

Bose-Einstein condensates and spectral properties of multicomponent nonlinear Schrödinger equations

Vladimir S. Gerdjikov^1,

1.
Institute for Nuclear Research and Nuclear Energy, Bulgarian academy of sciences, 72 Tsarigradsko chaussee, 1784 Sofia

Received: September 30, 2009

Revised: November 30, 2009

Published: September 2011

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Abstract

We analyze the properties of the soliton solutions of a class of models describing one-dimensional BEC with spin $F$. We describe the minimal sets of scattering data which determine uniquely both the corresponding potential of the Lax operator and its scattering matrix. Next we give several reductions of these MNLS, derive their $N$-soliton solutions and analyze the soliton interactions. Finally we prove an important theorem proving that if the initial conditions satisfy the reduction then one gets a solution of the reduced MNLS.

Keywords:

Bose-Einstein condensates,
Multicomponent nonlinear Schrödinger equations,
Soliton solutions,
Soliton interactions,
Reductions of MNLS.

Mathematics Subject Classification: Primary: 35Q51, 37K40; Secondary: 34K17.

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References

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