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Quasi-periodic solutions for class of Hamiltonian partial differential equations with fixed constant potential

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Abstract

We consider Hamiltonian partial differential equations u tt +|∂ x u|+σu = f(u); x ∈ T; t ∈ ℝ; with periodic boundary conditions, where f(u) is a real-analytic function of the form f(u) = u5 + o(u5) near u = 0; σ ∈ (0; 1) is a fixed constant, and T = ℝ/2πℤ: A family of quasi-periodic solutions with 2-dimensional are constructed for the equation above with π ∈ (0; 1)ℚ: The proof is based on infinite-dimensional KAM theory and partial Birkhoff normal form.

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Authors and Affiliations

  1. School of Mathematics, Southeast University, Nanjing, 211189, China

    Xindong Xu

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  1. Xindong Xu
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Xu, X. Quasi-periodic solutions for class of Hamiltonian partial differential equations with fixed constant potential. Front. Math. China 13, 227–254 (2018). https://doi.org/10.1007/s11464-017-0667-7

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  • DOI: https://doi.org/10.1007/s11464-017-0667-7

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