CHAOTIC OSCILLATIONS OF THE KLEIN-GORDON EQUATION WITH DISTRIBUTED ENERGY PUMPING AND VAN DER POL BOUNDARY REGULATION AND DISTRIBUTED TIME-VARYING COEFFICIENTS
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2014 Texas State University - San Marcos. 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.
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS
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