可积的（1+1）Gross-Pitaevskii方程的任意维数混沌推广
Extension of the integrable, (1+1) Gross-Pitaevskii equation to chaotic behaviour and arbitrary dimensions
摘要：
将具有厄米特性质的可积（1+1）Gross-Pitaevskii（GP-）方程作为一般复域的一部分，在拉克斯对的sl（2，C）代数中推广到混沌行为.此外，我们还证明了具有任意外部势的GP型方程的守恒量的对合性质。我们将拉克斯对矩阵的方法推广到任意时空维，并从基础代数的结构常数中得出非线性方程的类型。我们也可以从（N-1）维基空间内的循环和到一般SL（n，C）群或子群的流形的映射计算守恒量，只要所得的纤维空间是非平凡同伦类。
英文摘要：
The integrable, (1+1) Gross-Pitaevskii (GP-) equation with hermitian property is extended to chaotic behaviour as part of general complex fields within the sl(2,C) algebra for Lax pairs. Furthermore, we prove the involution property of conserved quantities in the case of GP-type equations with an arbitrary external potential. We generalize the approach of Lax pair matrices to arbitrary spacetime dimensions and conclude for the type of nonlinear equations from the structure constants of the underlying algebra. One can also calculate conserved quantities from loops within the (N-1) dimensional base space and the mapping to the manifold of the general SL(n,C) group or a sub-group, provided that the resulting fibre space is of nontrivial homotopic kind.
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