In this letter, abundant families of Jacobi elliptic function
envelope solutions of the N-coupled nonlinear Schrödinger
(NLS) system are obtained directly. When the modulus m →
1, those periodic solutions degenerate as the corresponding
envelope soliton solutions, envelope shock wave solutions.
Especially, for the 3-coupled NLS system, five types of Jacobi
elliptic function envelope solutions are illustrated both
analytically and graphically. Two types of those degenerate as
envelope soliton solutions.
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