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In this paper we consider the spectral and nonlinear stability of periodic traveling wave solutions of a generalized Kuramoto-Sivashinsky equation. In particular, we resolve the long-standing question of nonlinear modulational stability by…
The stability properties of line solitary wave solutions of the (2+1)-dimensional Boussinesq equation with respect to transverse perturbations and their consequences are considered. A geometric condition arising from a multi-symplectic…
The new perturbation theory for the problem of nonstationary anharmonic oscillator with polynomial nonstationary perturbation is proposed. As a zero order approximation the exact wave function of harmonic oscillator with variable frequency…
We study nonlinear mixing effects among quadrupole modes and scissors modes in a harmonically trapped Bose-Einstein condensate. Using a perturbative technique in conjunction with a variational approach with a Gaussian trial wave function…
We present a novel geometric approach for determining the unique structure of a Hamiltonian and establishing an instability criterion for quantum quadratic systems. Our geometric criterion provides insights into the underlying geometric…
We study the inhibition of pattern formation in nonlinear optical systems using intracavity photonic crystals. We consider mean field models for single and doubly degenerate optical parametric oscillators. Analytical expressions for the new…
The nonlinear evolution of the Weibel instability driven by the anisotropy of the electron distribution function in a collisionless plasma is investigated in a spatially one-dimensional configuration with a Vlasov code in a two-dimensional…
A modal stability analysis shows that plane Poiseuille flow of an Oldroyd-B fluid becomes unstable to a `center mode' with phase speed close to the maximum base-flow velocity, $U_{max}$. The governing dimensionless groups are the Reynolds…
A stability analysis is made for a non-singular pre-big-bang like cosmological model based on 1-loop corrected string effective action. Its homogeneous and isotropic solution realizes non-singular transition from de Sitter universe to…
I utilize the Petrov-Galerkin formulation and develop a new method for solving the unsteady collisionless Boltzmann equation in both the linear and nonlinear regimes. In the first order approximation, the method reduces to a linear…
The stability of plane Poiseuille flow of a viscous Newtonian fluid in a multilayer channel with anisotropic porous walls is analyzed using the classical modal analysis, the energy method, and the non-modal analysis. The influence of porous…
We propose a classification of bifurcations of Vlasov equations, based on the strength of the resonance between the unstable mode and the continuous spectrum on the imaginary axis. We then identify and characterize a new type of generic…
Nonlinear normal modes are periodic orbits that survive in nonlinear many-body Hamiltonian systems, and their instability is crucial for relaxation dynamics. Here, we study the instability process of the $\pi/3$-mode in the…
An analytical variational method is applied to the molecular Holstein Hamiltonian in which the dispersive features of the dimension dependent phonon spectrum are taken into account by a force constant approach. The crossover between a large…
We experimentally demonstrate synthesis and in-situ analysis of multimode plasmonic excitations in two-wire transmission lines supporting a symmetric and an antisymmetric eigenmode. To this end we irradiate an incoupling antenna with a…
The conductance of a disordered finite-size electron system is calculated by reducing the initial dynamic problem of arbitrary dimensionality to strictly one-dimensional problems for one-particle mode propagators. The metallic ground state…
The non-linear Hall term present in the induction equation in the electron-magneto-hydrodynamics limit is responsible for the Hall drift of the magnetic field and, in some cases, for the so-called Hall instability. We investigate whether or…
We study the stability and the modes of non -- isothermal coronal loop models with different intensity values of the equilibrium twisted magnetic field.We use an energy principle obtained via non -- equilibrium thermodynamic arguments. The…
We present a study of three-mode parametric instability in large-scale gravitational-wave detectors. Previous work used a linearised model to study the onset of instability. This paper presents a non-linear study of this phenomenon, which…
We present a general result of transverse nonlinear instability of 1-d solitary waves for Hamiltonian PDE's for both periodic or localized transverse perturbations. Our main structural assumption is that the linear part of the 1d model and…