几个耦合离散模型的任意阶Lame多项式解
Solutions of Several Coupled Discrete Models in terms of Lame Polynomials of Arbitrary Order
摘要：
耦合离散模型在物理学的几个领域中大量存在。在这里，我们提供了一个广泛的精确的拟周期解的数量耦合离散模型的任意阶的Lamé多项式。所讨论的模型是（i）耦合Salerno模型，（ii）耦合Ablowitz-Ladik模型，（iii）耦合$ϕ^4$模型，（iv）耦合$ϕ^6$模型。在所有这些情况下，我们表明，系数的Lamé多项式是这样的Lamé多项式可以重新表示在Chebyshev多项式的相关Jacobi椭圆函数。
英文摘要：
Coupled discrete models abound in several areas of physics. Here we provide an extensive set of exact quasiperiodic solutions of a number of coupled discrete models in terms of Lamé polynomials of arbitrary order. The models discussed are (i) coupled Salerno model, (ii) coupled Ablowitz-Ladik model, (iii) coupled $ϕ^4$ model, and (iv) coupled $ϕ^6$ model. In all these cases we show that the coefficients of the Lamé polynomials are such that the Lamé polynomials can be reexpressed in terms of Chebyshev polynomials of the relevant Jacobi elliptic function.
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