# $CPT$-symmetric coupler with intermodal dispersion

## TL;DR

This paper explores a $CPT$-symmetric dual-core waveguide with intermodal dispersion, demonstrating stable vector solitons and unique dynamics resulting from the interplay of gain, loss, and dispersive coupling.

## Contribution

It introduces a $CPT$-symmetric coupler model with second-order dispersion, revealing stable soliton solutions and complex stability behaviors not previously reported.

## Key findings

- Stable vector solitons supported by second-order dispersion.
- Existence of complex stationary two-hump solutions.
- Unusual decay dynamics of unstable solitons.

## Abstract

A dual-core waveguide with balanced gain and loss in different arms and with intermodal coupling is considered. The system is not invariant under the conventional $PT$ symmetry but obeys $CPT$ symmetry where an additional spatial inversion $C$ corresponds to swapping the coupler arms. We show that second-order dispersion of coupling allows for unbroken $CPT$ symmetry and supports propagation of stable vector solitons along the coupler. Small-amplitude solitons are found in explicit form. The combined effect of gain-and-loss and dispersive coupling results in several interesting features which include a separation between the components in different arms, nontrivial dependence of stability of a soliton on its velocity, and the existence of more complex stationary two-hump solutions. Unusual decay dynamics of unstable solitons is discussed too.