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This study introduces generalized nonlinear Schrödinger equations with complex Wadati-type potentials, revealing new models with unique properties like soliton families and symmetry breaking. These findings enhance understanding of nonlinearity and non-Hermiticity in physical systems.

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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.