8 papers
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…
Instability mechanisms on asymptotically AdS black hole backgrounds
Filip Ficek, Maciej Maliborski
We investigate dynamics of the conformal scalar equation with defocusing cubic nonlinearity and Robin boundary conditions on the Reissner-Nordström-anti-de Sitter background. At c…
Nonlinear oscillations of strings and beams
Filip Ficek, Maciej Maliborski
We investigate the time-periodic solutions to the nonlinear wave and beam equations and uncover their intricate, fractal-like structure. In particular, we identify a new class of l…
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…
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…
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…