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Reduction and chaotic behavior of point vortices on a plane and a sphere
New periodic solutions for three or four identical vortices on a plane and a sphere
1. | Institute of Computer Science, Udmurt State University, 426034 Izhevsk |
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Carlos García-Azpeitia. Relative periodic solutions of the $ n $-vortex problem on the sphere. Journal of Geometric Mechanics, 2019, 11 (3) : 427-438. doi: 10.3934/jgm.2019021 |
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Chjan C. Lim, Ka Kit Tung. Introduction: Recent advances in vortex dynamics and turbulence. Discrete and Continuous Dynamical Systems - B, 2005, 5 (1) : i-i. doi: 10.3934/dcdsb.2005.5.1i |
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Zhongyi Huang, Peter A. Markowich, Christof Sparber. Numerical simulation of trapped dipolar quantum gases: Collapse studies and vortex dynamics. Kinetic and Related Models, 2010, 3 (1) : 181-194. doi: 10.3934/krm.2010.3.181 |
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Hans G. Kaper, Peter Takáč. Bifurcating vortex solutions of the complex Ginzburg-Landau equation. Discrete and Continuous Dynamical Systems, 1999, 5 (4) : 871-880. doi: 10.3934/dcds.1999.5.871 |
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Francesco Paparella, Alessandro Portaluri. Geometry of stationary solutions for a system of vortex filaments: A dynamical approach. Discrete and Continuous Dynamical Systems, 2013, 33 (7) : 3011-3042. doi: 10.3934/dcds.2013.33.3011 |
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Shijin Ding, Qiang Du. The global minimizers and vortex solutions to a Ginzburg-Landau model of superconducting films. Communications on Pure and Applied Analysis, 2002, 1 (3) : 327-340. doi: 10.3934/cpaa.2002.1.327 |
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Zhixian Yu, Rong Yuan, Shaohua Gan. Novel entire solutions in a nonlocal 2-D discrete periodic media for bistable dynamics. Discrete and Continuous Dynamical Systems - B, 2021, 26 (9) : 4815-4838. doi: 10.3934/dcdsb.2020314 |
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Anne de Bouard, Reika Fukuizumi, Romain Poncet. Vortex solutions in Bose-Einstein condensation under a trapping potential varying randomly in time. Discrete and Continuous Dynamical Systems - B, 2015, 20 (9) : 2793-2817. doi: 10.3934/dcdsb.2015.20.2793 |
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Lipeng Duan, Jun Yang. On the non-degeneracy of radial vortex solutions for a coupled Ginzburg-Landau system. Discrete and Continuous Dynamical Systems, 2021, 41 (10) : 4767-4790. doi: 10.3934/dcds.2021056 |
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Elvira Zappale. A note on dimension reduction for unbounded integrals with periodic microstructure via the unfolding method for slender domains. Evolution Equations and Control Theory, 2017, 6 (2) : 299-318. doi: 10.3934/eect.2017016 |
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Guo Lin, Shuxia Pan. Periodic traveling wave solutions of periodic integrodifference systems. Discrete and Continuous Dynamical Systems - B, 2020, 25 (8) : 3005-3031. doi: 10.3934/dcdsb.2020049 |
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José Luis Bravo, Manuel Fernández, Antonio Tineo. Periodic solutions of a periodic scalar piecewise ode. Communications on Pure and Applied Analysis, 2007, 6 (1) : 213-228. doi: 10.3934/cpaa.2007.6.213 |
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Xiaoyan Lin, Xianhua Tang. Solutions of nonlinear periodic Dirac equations with periodic potentials. Discrete and Continuous Dynamical Systems - S, 2019, 12 (7) : 2051-2061. doi: 10.3934/dcdss.2019132 |
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