Related papers: Weakly nonlinear analysis in spatially extended sy…
A perturbative formula for the lowest Lyapunov exponent of an Anderson model on a strip is presented. It is expressed in terms of an energy dependent doubly stochastic matrix, the size of which is proportional to the strip width. This…
The late stages of large-scale structure evolution are treated semi-analytically within the framework of modified halo model. We suggest simple yet accurate approximation for relating the non-linear amplitude to linear one for spherical…
A new statistical field-theory model of isotropic turbulence is introduced. The model renormalizes the effects of turbulent stresses into a velocity-gradient-dependent random force. The model is well-defined within the context of the…
A hard-core disordered boson system is mapped onto a quantum spin 1/2 XY-model with transverse random fields. It is then generalized to a system of spins with an arbitrary magnitude S and studied through a 1/S expansion. The first order 1/S…
We address the problem of constructing a non-equilibrium stationary state for a one-dimensional stochastic Klein-Gordon wave equation with non-linearity, using perturbation theory. The linear theory is reviewed, but with the linear…
The modulational instability of broadband optical pulses in a four-state atomic system is investigated. In particular, starting from a recently derived generalized nonlinear Schr\"odinger equation, a wave-kinetic equation is derived. A…
In this paper, we study modulation instabilities (MI) in a one-dimensional chain configuration of a flexible mechanical metamaterial (flexMM). Using the lumped element approach, flexMMs can be modeled by a coupled system of discrete…
We consider linear instability of solitary waves of several classes of dispersive long wave models. They include generalizations of KDV, BBM, regularized Boussinesq equations, with general dispersive operators and nonlinear terms. We obtain…
A mathematical model describing the initial stage of the capture of oscillatory systems into autoresonance under the action of slowly varying pumping is considered. Solutions with an infinitely growing amplitude are associated with the…
We study a wave equation with a nonlocal time fractional damping term that models the effects of acoustic attenuation characterized by a frequency dependence power law. First we prove existence of a unique solution to this equation with…
We give a pedagogical review of a covariant and fully non-perturbative approach to study nonlinear perturbations in cosmology. In the first part, devoted to cosmological fluids, we define a nonlinear extension of the uniform-density…
A continuous sequence of infinitesimal unitary transformations is used to diagonalize the quantum sine-Gordon model for \beta^2\in(2\pi,\infty). This approach can be understood as an extension of perturbative scaling theory since it links…
We extend the theory of spectral submanifolds (SSMs) to general non-autonomous dynamical systems that are either weakly forced or slowly varying. Examples of such systems arise in structural dynamics, fluid-structure interactions and…
We consider reduction of dimension for nonlinear dynamical systems. We demonstrate that in some cases, one can reduce a nonlinear system of equations into a single equation for one of the state variables, and this can be useful for…
Dynamical systems theory has long provided a foundation for understanding evolving phenomena across scientific domains. Yet, the application of this theory to complex real-world systems remains challenging due to issues in mathematical…
This paper is devoted to the convergence and stability analysis of a class of nonlinear subdivision schemes and associated multi-resolution transforms. These schemes are defined as a perturbation of a linear subdivision scheme. Assuming a…
We present a general formalism that allows for the computation of large-order renormalized expansions in the spacetime representation, effectively doubling the numerically attainable perturbation order of renormalized Feynman diagrams. We…
Characterizing the emergence of chaotic dynamics of complex networks is an essential task in nonlinear science with potential important applications in many fields such as neural control engineering, microgrid technologies, and ecological…
Infinitesimal and finite amplitude error propagation in spatially extended systems are numerically and theoretically investigated. The information transport in these systems can be characterized in terms of the propagation velocity of…
The dynamical behaviours of a kinetically constrained spin model (Fredrickson-Andersen model) on a Bethe lattice are investigated by a perturbation analysis that provides exact final states above the nonergodic transition point. It is…