Existence diagrams and excitations of vector Akhmediev breathers with self-steepening.

Abstract

We revisit vector breathers with self-steepening in both focusing and defocusing regimes. We present previously unknown existence diagrams of Akhmediev breathers in a frequency-wave-number plane, which can be used to identify a family of nondegenerate second-order Akhmediev breathers in the focusing regime. The existence diagrams are extracted from the exact solutions where we modify the Lax pair to obtain a simple one-to-one correspondence between the square Lax spectral parameter and eigenvalues. Based on the existence diagrams, unique excitations of nondegenerate second-order Akhmediev breathers are predicted. Their role in the nonlinear stage of modulation instability is revealed. In particular, numerical simulations starting from a nonideal initial condition with either single- or two-component modulations confirm our theoretical prediction.