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Time-periodic solutions to the cubic wave equation: an elementary constructive approach
Filip Ficek
We present an elementary proof of existence of infinite family of time-periodic solutions to the one-dimensional nonlinear cubic wave equation with Dirichlet boundary conditions. I…
New class of time-periodic solutions to the 1D cubic wave equation
Filip Ficek, Maciej Maliborski
In recent papers (arXiv:2407.16507, arXiv:2408.05158) we presented results suggesting the existence of a new class of time-periodic solutions to the defocusing cubic wave equation…
Complex structure of time-periodic solutions decoded in Poincaré-Lindstedt series: the cubic conformal wave equation on
Filip Ficek, Maciej Maliborski
This work explores the rich structure of spherically symmetric time-periodic solutions of the cubic conformal wave equation on . We discover that the families of so…
Trees, trunks, and branches -- bifurcation structure of time-periodic solutions to
Filip Ficek, Maciej Maliborski
We propose a systematic approach to analysing the complex structure of time-periodic solutions to the cubic wave equation on an interval with Dirichlet boundary conditions first re…
Periodic Solutions for the 1d Cubic Wave Equation with Dirichlet Boundary Conditions
Filip Ficek, Maciej Maliborski
We study time-periodic solutions for the cubic wave equation on an interval with Dirichlet boundary conditions. We begin by following the perturbative construction of Vernov and Kh…