科研之友
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摘要
In this paper, the determinant representation of the n-fold binary Darboux transformation, which is a 2 x 2 matrix, for the Ablowitz-Kaup-Newell-Segur equation is constructed. In this 2 x 2 matrix, each element is expressed by (2n+1)-order determinants. When the reduction condition r = -(q) over bar is considered, we obtain one of binary Darboux transformations for the nonlinear Schrodinger (NLS) equation. As its applications, several solutions are constructed for the NLS equation. Especially, a new form of two-soliton is given explicitly.
