Nonlinear waves in networks: model reduction for the sine-Gordon equation
Jean-Guy Caputo1, Denys Dutykh2
1Laboratoire de Mathématiques, INSA de Rouen, 76801 Saint-Etienne du Rouvray, France.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 13, 2014
Summary
Nonlinear waves like kinks and breathers can cross junctions. A one-dimensional model accurately predicts their behavior, with kinks needing energy and breathers crossing based on velocity and frequency.
Area of Science:
- Physics
- Applied Mathematics
Background:
- Nonlinear waves are crucial in various physical systems.
- Understanding wave propagation through junctions is key to many applications.
Purpose of the Study:
- To investigate the propagation of nonlinear waves across Y- and T-type junctions.
- To develop and validate a simplified model for predicting wave behavior.
Main Methods:
- Utilized the two-dimensional (2D) sine-Gordon equation as a model.
- Simulated the crossing of kinks and breathers at junctions.
- Developed a one-dimensional (1D) effective model for comparison.
Main Results:
- Junction geometry (fork angle) had no impact on wave crossing for small widths.
- The 1D effective model showed strong agreement with 2D simulations.
- Kinks cross junctions with sufficient energy; breathers cross when velocity exceeds a threshold related to frequency.
Conclusions:
- A simplified 1D model effectively captures complex 2D nonlinear wave dynamics at junctions.
- Established clear criteria for kink and breather wave transmission.
- The methodology is adaptable to other nonlinear wave models.
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