Unbreakable $\mathcal{PT}$ symmetry of exact solitons supported by transversally modulated nonlinearity acting as a psuedopotential

TL;DR

This paper analytically and numerically demonstrates the existence of unbreakable $ ext{PT}$-symmetric solitons supported by a transversally modulated defocusing nonlinearity acting as a pseudopotential, ensuring unbroken $ ext{PT}$ symmetry.

Contribution

It introduces a novel class of exact $ ext{PT}$-symmetric solitons supported by a transversally modulated defocusing nonlinearity, showing $ ext{PT}$ symmetry remains unbroken without linear refractive-index modulation.

Findings

Exact solitons in double-kink and fractional-transform forms identified.

$ ext{PT}$ symmetry remains unbroken in the system.

Transversally modulated defocusing nonlinearity is essential for $ ext{PT}$ symmetry.

Abstract

We demonstrate analytically and numerically the existence of exact solitons in the form of double-kink and fractional-transform, supported by a symmetric transversally modulated defocusing nonlinearity acting as a psuedopotential combined with an antisymmetric gain-loss profile. We explicate here that the $\mathcal{PT}$ symmetry is never broken in the dynamical system under study, even in the absence of any symmetric modulation of linear refractive-index, and the transversally modulated defocusing nonlinearity comes in the way as a requirement to establish the ensuing $\mathcal{PT}$ symmetry.