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Collapse in a forced three-dimensional nonlinear Schrodinger equation
1Landau Institute for Theoretical Physics, Kosygin Street 2, Moscow, 117334, Russia.
Summary
Sufficient conditions for collapse in a forced nonlinear Schrödinger equation were derived. Numerical studies extended these findings to cases with finite dissipation, revealing crucial insights into wave behavior.
Area of Science:
- Physics
- Applied Mathematics
- Nonlinear Dynamics
Background:
- The nonlinear Schrödinger equation (NLSE) is a fundamental model in various scientific fields, including optics and Bose-Einstein condensates.
- Understanding the conditions leading to wave collapse is crucial for predicting system behavior and preventing catastrophic events.
Purpose of the Study:
- To establish rigorous mathematical conditions for the occurrence of collapse in a forced three-dimensional NLSE.
- To investigate the impact of finite dissipation on the collapse dynamics predicted by the dissipationless model.
Main Methods:
- Derivation of sufficient conditions for collapse using analytical techniques.
- Numerical simulations of the forced three-dimensional NLSE with varying levels of dissipation.
Main Results:
- Sufficient conditions for collapse were analytically derived for the dissipationless forced NLSE.
- Numerical results confirmed and extended the analytical findings, showing that finite dissipation can influence or prevent collapse.
Conclusions:
- The study provides a theoretical framework for understanding collapse in forced NLSE.
- Numerical evidence highlights the significant role of dissipation in modulating collapse phenomena.
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