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Transparent boundary condition for simulating rogue wave solutions in the nonlinear Schrödinger equation
Chenxi Zheng1, Shaoqiang Tang1
1Key Laboratory of High Energy Density Physics Simulations, Ministry of Education, State Key Laboratory of Turbulence and Complex Systems, College of Engineering, Peking University, Beijing 100871, China.
Physical Review. E
|December 23, 2022
Summary
New transparent boundary conditions significantly reduce computational domain size for simulating rogue waves in nonlinear Schrödinger equation models. This enhances accuracy and efficiency for Peregrine soliton and Kuznetsov-Ma breather solutions.
Area of Science:
- Numerical analysis
- Computational physics
- Nonlinear dynamics
Background:
- Simulating rogue waves in nonlinear systems requires accurate numerical boundary conditions.
- Existing methods often necessitate large computational domains, increasing resource demands.
- The nonlinear Schrödinger equation is a key model for studying wave phenomena.
Purpose of the Study:
- To develop and propose novel transparent boundary conditions for rogue wave solutions.
- To enable accurate simulations using smaller computational domains.
- To improve the efficiency of numerical simulations for specific wave solutions.
Main Methods:
- Construction of transparent boundary conditions tailored for Peregrine soliton solutions.
- Construction of transparent boundary conditions tailored for Kuznetsov-Ma breather solutions.
- Implementation and comparison with existing boundary condition methods using the Crank-Nicolson scheme.
Main Results:
- Proposed boundary conditions achieve "acceptable accuracy" with significantly smaller computational domains.
- For Peregrine solitons, the domain size is reduced by a factor of 16.
- Reduced domain size leads to decreased memory requirements and computation time.
Conclusions:
- Transparent boundary conditions offer a more efficient approach for simulating specific rogue wave solutions.
- These methods are particularly advantageous for the Peregrine soliton.
- The findings pave the way for more accessible and faster simulations in nonlinear wave research.
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