Related Experiment Video
Updated: Feb 25, 2026

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
Published on: May 27, 2020
The nonlinear Schrödinger equation with generalized nonlinearities and PT-symmetric potentials: Stable solitons,
1Key Laboratory of Mathematics Mechanization, Institute of Systems Science, AMSS, Chinese Academy of Sciences, Beijing 100190, China and School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China.
Abstract:
We investigate the nonlinear Schrödinger (NLS) equation with generalized nonlinearities and complex non-Hermitian potentials and present the novel parity-time-( PT-) symmetric potentials for the NLS equation with power-law nonlinearities supporting some bright solitons. For distinct types of PT-symmetric potentials including Scarf-II, Hermite-Gaussian, and asymptotically periodic potentials, we, respectively, explore the phase transitions for the linear Hamiltonian operators. Moreover, we analytically find stable bright solitons in the generalized NLS equations with several types of PT-symmetric potentials, and their stability is corroborated by the linear stability spectrum and direct wave-propagation simulations. Interactions of two solitons are also explored. More interestingly, we find that the nonlinearity can excite the unstable linear modes (i.e., possessing broken linear PT-symmetric phase) to stable nonlinear modes. The results may excite potential applications in nonlinear optics, Bose-Einstein condensates, and relevant fields.
Related Concept Videos
Linear Approximation in Time Domain
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
Linear Approximation in Frequency Domain
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
Oscillations about an Equilibrium Position
The Quantum-Mechanical Model of an Atom
Poisson's And Laplace's Equation
Molecular Orbital Theory II

