Nonstandard bilinearization of $\mathcal{P}\mathcal{T}$-invariant nonlocal nonlinear Schrödinger equation: Bright soliton solutions

Abstract

In this paper, we succeed to bilinearize the $\mathcal{P}\mathcal{T}$-invariant nonlocal nonlinear Schrödinger (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 $\mathcal{P}\mathcal{T}$-invariant multi-soliton solutions.

arXiv comment13 pages, 2 figures, Accepted for Publication in Physics Letters A

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• On symmetry preserving and symmetry broken bright, dark and antidark soliton solutions of nonlocal nonlinear Schrödinger equation
• Nonlocal Nonlinear Schrodinger Equation on Metric Graphs
• General $N$-solitons and their dynamics in several nonlocal nonlinear Schrödinger equations
• Multicomplex solitons
• Dynamics of high-order solitons in the nonlocal nonlinear Schrödinger equations
• Darboux transformations and solutions of nonlocal Hirota and Maxwell-Bloch equations