Breather solutions of the nonlocal nonlinear self-focusing Schrödinger equation

Abstract

The first- and second-order breather solutions of the self-focusing nonlocal nonlinear Schrödinger (NNLS) equation are obtained by employing Hirota's bilinear method. The NNSE also happens to be an example of Schrödinger equation with parity-time (PT) symmetry. With the help of recurrence relations in the Hirota bilinear form, the nth-order breather solutions on the nonzero background of the NNLS equation are obtained, and the collision, superposition and separation of transmission modes is studied respectively. When the parameters describing these breathers are selected as some special values, they display plentiful spatial structures which provide effective methods for controlling the localized optical waves in nonlocal nonlinear media.