Related papers: Spectra and Bifurcations
We study the effect of external stochastic modulation on a system with O(2) symmetry that exhibits a Hopf or oscillatory instability in the absence of modulation. The study includes a random component in both the control parameter of the…
Several analysis methods for nonstationary fluctuations are described and applied to the edge localized mode (ELM) instabilities of limiter H-mode plasmas. The microwave scattering diagnostic observes poloidal $k_{\theta}$ values of 3.3…
We consider a nonlinear wave equation with nonconstant coefficients. In particular, the coefficient in front of the second order space derivative is degenerate. We give the blow-up behavior and the regularity of the blow-up set. Partial…
We examine examples of weakly nonlinear systems whose steady states undergo a bifurcation with increasing forcing, such that a forced subsystem abruptly ceases to absorb additional energy, instead diverting it into an initially quiescent,…
Many physical systems can be described by nonlinear eigenvalues and bifurcation problems with a linear part that is non-selfadjoint e.g. due to the presence of loss and gain. The balance of these effects is reflected in an antilinear…
We study the modulational stability problem for the traveling periodic waves (called Stokes waves) in an infinitely deep fluid by using pseudo-differential operators in conformal variables. We derive the criteria and the normal forms for…
We study symmetry breaking of solitons in the framework of a nonlinear fractional Schr\"{o}dinger equation (NLFSE), characterized by its L\'{e}vy index, with cubic nonlinearity and a symmetric double-well potential. Asymmetric, symmetric,…
The effect of multiplicative stochastic perturbations on Hamiltonian systems on the plane is investigated. It is assumed that perturbations fade with time and preserve a stable equilibrium of the limiting system. The paper investigates…
Synchronization among rhythmic elements is modeled by coupled phase-oscillators each of which has the so-called natural frequency. A symmetric natural frequency distribution induces a continuous or discontinuous synchronization transition…
We unveil instances where nonautonomous linear systems manifest distinct nonuniform $\mu$-dichotomy spectra despite admitting nonuniform $(\mu, \varepsilon)$-kinematic similarity. Exploring the theoretical foundations of this lack of…
To explore resonance phenomena in the nonlinear region, we show by experimental measurements and theoretical analyses that resonance happens in modulation instability (MI) from non-instantaneous nonlinearities in photorefractive crystals.…
We study stability and dynamics of the single cylindrically symmetric solitary structures and dipolar solitonic molecules in spatially nonlocal media. The main properties of the solitons, vortex solitons, and dipolar solitons are…
Saddle-node bifurcations arise frequently in solitary waves of diverse physical systems. Previously it was believed that solitary waves always undergo stability switching at saddle-node bifurcations, just as in finite-dimensional dynamical…
A new class of solitary waves arises in the solution of nonlinear wave equations with constant impedance and no dispersive terms. They depend on a balance between nonlinearity and a dispersion-like effect due to spatial variation in the…
Continuous families of solitons in generalized nonlinear Sch\"odinger equations with non-PT-symmetric complex potentials are studied analytically. Under a weak assumption, it is shown that stationary equations for solitons admit a constant…
Period doubling is a universal bifurcation of central importance in all disciplines of nonlinear science, which generally signals the existence of chaotic dynamics in the vicinity of the system parameters. Although observed in diverse…
Since the parity-time-(PT-) symmetric quantum mechanics was put forward, fundamental properties of some linear and nonlinear models with PT-symmetric potentials have been investigated. However, previous studies of PT-symmetric waves were…
We consider the model of a dual-core spatial-domain coupler with chi^(2) and chi^(3) nonlinearities acting in two parallel cores. We construct families of symmetric and asymmetric solitons in the system with self-defocusing chi^(3) terms,…
We study transitions from convective to absolute instability near a trivial state in large bounded domains for prototypical model problems in the presence of transport and negative nonlinear feedback. We identify two generic scenarios,…
With the recent development of analytical methods for studying the collective dynamics of coupled oscillator systems, the dynamics of communities of coupled oscillators have received a great deal of attention in the nonlinear dynamics…