N-fold Darboux Transformation for Integrable Couplings of AKNS Equations

摘要

For the integrable couplings of Ablowitz-Kaup-Newell-Segur (ICAKNS) equations,N-fold Darboux trans formation (DT) TN,which is a 4 × 4 matrix,is constructed in this paper.Each element of this matrix is expressed by ratio of the (4N + 1)-order determinant and 4N-order determinant of eigenfunctions.By making use of these formulae the determinant expressions of N-transformed new solutions p[N],q[N],r[N] and s[N] are generated by this N-fold DT Furthermore,when the reduced conditions q =-p* and s =-r* are chosen,we obtain determinant representation of N-fold DT and N-transformed solutions for the integrable couplings of nonlinear Schr(o)dinger (ICNLS) equations Starting from the zero seed solutions,one-soliton solutions are explicitly given as an example.