玻色-爱因斯坦凝聚体与多元非线性薛定谔方程的谱性质
Bose-Einstein Condensates and spectral properties of multicomponent nonlinear Schrodinger equations
摘要：
本文分析了一类描述自旋为F的一维BEC模型的孤子解的性质。我们描述的散射数据的最小集，唯一地确定相应的潜在的拉克斯运营商和它的散射矩阵。接下来我们给出了这些MNLS的几种约化，导出了它们的N孤子解，并分析了孤子间的相互作用。最后，我们证明了一个重要的定理，证明了如果初始条件满足约简，那么就可以得到约简MNLS的解。
英文摘要：
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.
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