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Magnetically Induced Rotating Rayleigh-Taylor Instability
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Modulation instability and rogue waves for two and three dimensional nonlinear Klein-Gordon equation
Zhiqiang Yang1, Gui Mu1, Zhenyun Qin2
1School of Mathematics, Kunming University, Kunming, Yunnan 650214, People's Republic of China.
Chaos (Woodbury, N.Y.)
|September 23, 2024
Summary
This study analyzes modulation instability in 2D and 3D nonlinear Klein-Gordon equations, revealing conditions for rogue wave formation. Researchers constructed N-breathers and high-order rogue waves, finding their dynamics align with the nonlinear Schrödinger equation.
Area of Science:
- Nonlinear Dynamics
- Mathematical Physics
- Wave Phenomena
Background:
- The nonlinear Klein-Gordon equation models various physical systems.
- Understanding wave propagation and stability is crucial in nonlinear systems.
- Previous studies have explored solitons and breathers in related equations.
Purpose of the Study:
- To perform modulation instability analysis on 2D and 3D nonlinear Klein-Gordon equations.
- To construct N-breathers and high-order rogue waves.
- To investigate the dynamic behaviors and conditions for the existence of these waves.
Main Methods:
- Modulation instability analysis.
- Construction of N-breathers from 2N-solitons.
- Bilinear method combined with improved long-wave limit technique.
- Analysis of explicit expressions for rogue waves and lumps.
Main Results:
- Instability regions depend on dispersion and wavenumbers.
- Breather dynamics in 2D align with modulation instability analysis.
- General high-order rogue waves and rational solutions were obtained for 2D and 3D equations.
- Rogue waves are shown to always exist under specific conditions.
Conclusions:
- Modulation instability analysis provides insights into wave behavior.
- The nonlinear Klein-Gordon equation supports complex wave structures like breathers and rogue waves.
- Explicit solutions confirm the general existence of rogue waves in 2D and 3D systems.
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