Periodic travelling waves in convex Klein–Gordon chains |
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Authors: | Michael Herrmann |
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Institution: | aOxford Centre for Nonlinear PDE, Mathematical Institute, University of Oxford, 24–29 St Giles’, OX1 3LB Oxford, United Kingdom |
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Abstract: | We study Klein–Gordon chains with attractive nearest neighbour forces and convex on-site potential, and show that there exists a two-parameter family of periodic travelling waves (wave trains) with unimodal and even profile functions. Our existence proof is based on a saddle-point problem with constraints and exploits the invariance properties of an improvement operator. Finally, we discuss the numerical computation of wave trains. |
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Keywords: | Klein– Gordon chain Lattice travelling waves Constrained optimisation |
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