Bo Sun, Tingwen Huang
Abstract:
Consider the Klein-Gordon equation with variable coefficients, a
van der Pol cubic nonlinearity in one of the boundary conditions and
a spatially distributed antidamping term, we use a
variable-substitution technique together with the analogy with
the 1-dimensional wave equation to prove that for the Klein-Gordon
equation chaos occurs for a class of equations and boundary
conditions when system parameters enter a certain regime. Chaotic
and nonchaotic profiles of solutions are illustrated by computer
graphics.
Submitted August 1, 2014. Published September 10, 2014.
Math Subject Classifications: 35L05, 35L70, 58F39, 70L05.
Key Words: Chaotic Oscillations; Klein-Gordon equation;
distributed energy pumping; van der Pol boundary regulation.
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Bo Sun Department of Mathematics Changsha University of Science and Technology Changsha, Hunan, China email: sunbo1965@yeah.net |
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Tingwen Huang Science Program, Texas A&M University at Qatar Education City, Doha, Qatar email: tingwen.huang@qatar.tamu.edu |
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