Integrable and Superintegrable Klein-Gordon and Schr\"odinger Type Dimers

TL;DR

This paper introduces a broad class of integrable and superintegrable PT-symmetric dimers, including oscillator and nonlinear Schrödinger types, with Hamiltonians of arbitrary even order, expanding the understanding of their mathematical structure.

Contribution

The paper provides new classes of integrable and superintegrable dimers with arbitrary even order Hamiltonians, enhancing the theoretical framework of PT-symmetric nonlinear oscillators and Schrödinger systems.

Findings

Identified wide classes of integrable oscillator dimers

Developed integrable and superintegrable nonlinear Schrödinger dimers

Hamiltonians of arbitrary even order for these systems

Abstract

A $PT$-symmetric dimer is a two-site nonlinear oscillator or a nonlinear Schr\"odinger dimer where one site loses and the other site gains energy at the same rate. We present a wide class of integrable oscillator type dimers whose Hamiltonian is of arbitrary even order. Further, we also present a wide class of integrable and superintegrable nonlinear Schr\"odinger type dimers where again the Hamiltonian is of arbitrary even order.