Nonlinear Schrödinger equations with amplitude-dependent Wadati potentials

Area of Science:

• Nonlinear physics
• Quantum mechanics
• Mathematical physics

Background:

• Complex Wadati-type potentials exhibit unique features in non-Hermitian systems.
• Standard Wadati potentials are real-valued functions dependent on spatial coordinates.

Purpose of the Study:

• To generalize Wadati potentials by incorporating field amplitude dependence.
• To explore nonlinear Schrödinger-type problems with these generalized potentials.
• To investigate physical relevance and properties of the new models.

Main Methods:

• Introduction of a generalized Wadati potential form.
• Analysis of nonlinear Schrödinger-type equations.
• Numerical simulations to study model behavior.

Main Results:

• Generalized models inherit properties like continuous soliton families and constant-amplitude waves.
• Demonstration of symmetry-breaking bifurcations in parity-time symmetric models.
• Observation of eigenvalue quartets in linear-instability spectra.

Conclusions:

• The study expands the class of nonlinear, non-Hermitian systems with remarkable properties.
• Results deepen the understanding of the interplay between nonlinearity and non-Hermiticity.
• The generalized models offer new avenues for studying complex physical phenomena.