Related papers: Stability of Nonlinear Normal Modes in the FPU-$\b…
We investigate the connection between local and global dynamics in the Fermi -- Pasta -- Ulam (FPU) $\beta$ -- model from the point of view of stability of its simplest periodic orbits (SPOs). In particular, we show that there is a…
Nonlinear interaction between normal modes dramatically affects energy equipartition, heat conduction and other fundamental processes in extended systems. In their celebrated experiment Fermi, Pasta and Ulam (FPU, 1955) observed that in…
By combining results of Mizumachi on the stability of solitons for the Toda lattice with a simple rescaling and a careful control of the KdV limit we give a simple proof that small amplitude, long-wavelength solitary waves in the…
Commonly, thermal transport properties of one-dimensional systems are found to be anomalous. Here, we perform a numerical and theoretical study of the $\beta$-FPUT chain, considered a prototypical model for one-dimensional anharmonic…
Fermi, Pasta and Ulam observed, that the excitation of a low frequency normal mode in a nonlinear acoustic chain leads to localization in normal mode space on large time scales. Fast equipartition (and thus complete delocalization) in the…
The dispersive interacting waves in Fermi-Pasta-Ulam (FPU) chains of particles in \textit{thermal equilibrium} are studied from both statistical and wave resonance perspectives. It is shown that, even in a strongly nonlinear regime, the…
Thermalization in nonlinear systems is a central concept in statistical mechanics and has been extensively studied theoretically since the seminal work of Fermi, Pasta and Ulam (FPU). Using molecular dynamics and continuum modeling of a…
Consider an FPU chain composed of $N\gg 1$ particles, and endow the phase space with the Gibbs measure corresponding to a small temperature $\beta^{-1}$. Given a fixed $K<N$, we construct $K$ packets of normal modes whose energies are…
We give a qualitative explanation of the analog of the Fermi-Pasta-Ulam (FPU) recurrence in a one-dimensional focusing nonlinear Schrodinger equation (NLSE). That recurrence can be considered as a result of the nonlinear development of…
The linear response to temperature variations is well characterised for equilibrium systems but a similar theory is not available, for example, for inertial heat conducting systems, whose paradigm is the Fermi-Pasta-Ulam (FPU) model driven…
Instabilities are common phenomena frequently observed in nature, sometimes leading to unexpected catastrophes and disasters in seemingly normal conditions. The simplest form of instability in a distributed system is its response to a…
We demonstrate that the modulation instability of the zone boundary mode in a finite (periodic) Fermi-Pasta-Ulam chain is the necessary but not sufficient condition for the efficient energy transfer by localized excitations. This transfer…
Periodic orbits for the classical $\phi^4$ theory on the one dimensional lattice are systematically constructed by extending the normal modes of the harmonic theory, for periodic, fixed and free boundary conditions. Through the process, we…
We apply Wave Turbulence theory to describe the dynamics on nonlinear one-dimensional chains. We consider $\alpha$ and $\beta$ Fermi-Pasta-Ulam-Tsingou (FPUT) systems, and the discrete nonlinear Klein-Gordon chain. We demonstrate that…
We prove global existence and uniqueness of solutions of some important nonlinear lattices which include the Fermi-Pasta-Ulam (FPU) lattice. Our result shows (on a particular example) that the FPU lattice with high nonlinearity and its…
We consider the Fermi-Pasta-Ulam-Tsingou (FPUT) chain composed by $N \gg 1$ particles and periodic boundary conditions, and endow the phase space with the Gibbs measure at small temperature $\beta^{-1}$. Given a fixed ${1\leq m \ll N}$, we…
A finite (periodic) FPU chain is chosen as a convenient point for investigating the energy exchange phenomenon in nonlinear oscillatory systems. As we have recently shown, this phenomenon may occur as a consequence of the resonant…
We show numerically that including soft-sphere type collisions in the celebrated Fermi-Pasta-Ulam ($FPU$) chain completely alters the thermal transport characteristics. The resulting $FPU^C$ chains, while being momentum preserving, satisfy…
The Fermi-Pasta-Ulam problem was one of the first computational experiments. It has stirred the physics community since, and resisted a simple solution for half a century. The combination of straightforward simulations, efficient…
We will present a survey of low energy periodic Fermi-Pasta-Ulam chains with leading idea the "breaking of symmetry". The classical periodic FPU-chain (equal masses for all particles) was analysed by Rink in 2001 with main conclusions that…