1 citations · 4 across the 10 of their papers we have counts for
10 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 ce…
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…
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…
Instability of nonlinear scalar field on strongly charged asymptotically AdS black hole background
Filip Ficek, Maciej Maliborski
The conformally invariant scalar equation permits the Robin boundary condition at infinity of asymptotically-AdS spacetimes. We show how the dynamics of conformal cubic scalar fiel…
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…
Dynamics of nonlinear scalar field with Robin boundary condition on the Schwarzschild--Anti-de Sitter background
Filip Ficek, Maciej Maliborski
This work concerns the dynamics of conformal cubic scalar field on a Schwarzschild--anti-de Sitter background. The main focus is on understanding how it depends on the size of the…
Planar domain walls in black hole spacetimes
Filip Ficek, Patryk Mach
We investigate the behaviour of low-mass, planar domain walls in the so-called model of the scalar field on the Schwarzschild and Kerr backgrounds. We focus on a transit of a…