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Researchers established bulk-edge correspondence in nonlinear systems by introducing auxiliary eigenvalues. This reveals how topological edge states are inherited, even with nonlinear eigenvalue effects.

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Area of Science:

  • Condensed matter physics
  • Nonlinear dynamics
  • Topological materials

Background:

  • Topological phenomena are increasingly studied in both linear and nonlinear systems.
  • A key challenge is establishing bulk-edge correspondence under nonlinear eigenvalue conditions.
  • Existing theories often struggle with the complexities introduced by nonlinearity.

Purpose of the Study:

  • To establish the bulk-edge correspondence in nonlinear systems.
  • To investigate the role of nonlinear eigenvalues in topological phenomena.
  • To provide a theoretical framework for understanding topological edge states in nonlinear settings.

Main Methods:

  • Introduction of auxiliary eigenvalues to analyze topological properties.
  • Analysis of the inheritance of topological edge states from auxiliary eigenstates.
  • Examination of the conditions under which nonlinearity preserves topological features.

Main Results:

  • Auxiliary eigenvalues enable the establishment of bulk-edge correspondence in nonlinear systems.
  • Topological edge states of auxiliary eigenstates are inherited as physical edge states under weak nonlinearity.
  • Monotonicity of auxiliary eigenvalues is key for this topological inheritance.

Conclusions:

  • The study successfully bridges the gap in understanding bulk-edge correspondence for nonlinear systems.
  • Auxiliary eigenvalues offer a powerful tool for analyzing topological properties in the presence of nonlinearity.
  • This work paves the way for designing and understanding novel topological materials with nonlinear characteristics.