Dynamics of spiral waves in the complex Ginzburg–Landau equation in bounded domains

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2020-12-15

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Abstract

Multiple-spiral-wave solutions of the general cubic complex Ginzburg–Landau equation in bounded domains are considered. We investigate the effect of the boundaries on spiral motion under homogeneous Neumann boundary conditions, for small values of the twist parameter q. We derive explicit laws of motion for rectangular domains and we show that the motion of spirals becomes exponentially slow when the twist parameter exceeds a critical value depending on the size of the domain. The oscillation frequency of multiple-spiral patterns is also analytically obtained.

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10.1016/j.physd.2020.132699

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Aguareles, M, SJ Chapman and T Witelski (2020). Dynamics of spiral waves in the complex Ginzburg–Landau equation in bounded domains. Physica D: Nonlinear Phenomena, 414. pp. 132699–132699. 10.1016/j.physd.2020.132699 Retrieved from https://hdl.handle.net/10161/23398.

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Witelski

Thomas P. Witelski

Professor in the Department of Mathematics

My primary area of expertise is the solution of nonlinear ordinary and partial differential equations for models of physical systems. Using asymptotics along with a mixture of other applied mathematical techniques in analysis and scientific computing I study a broad range of applications in engineering and applied science. Focuses of my work include problems in viscous fluid flow, dynamical systems, and industrial applications. Approaches for mathematical modelling to formulate reduced systems of mathematical equations corresponding to the physical problems is another significant component of my work.


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