Nonstandard bilinearization of $\cal{PT}$-invariant nonlocal nonlinear Schr\"{o}dinger equation: Bright soliton solutions

Abstract

In this paper, we succeed to bilinearize the $\cal{PT}$-invariant nonlocal nonlinear Schr\"{o}dinger (NNLS) equation through a nonstandard procedure and present more general bright soliton solutions. We achieve this by bilinearizing both the NNLS equation and its associated parity transformed complex conjugate equation in a novel way. The obtained one and two soliton solutions are invariant under combined space and time reversal transformations and are more general than the known ones. Further, by considering the two-soliton solution we bring out certain novel interaction properties of the $\cal{PT}$-invariant multi-soliton solutions.