Related papers: Spectra and Bifurcations
The dichotomy spectrum is introduced for linear mean-square random dynamical systems, and it is shown that for finite-dimensional mean-field stochastic differential equations, the dichotomy spectrum consists of finitely many compact…
A number of physical processes show some form of bifurcation or periodic splintering of a single distribution into two new ones. Recently, it has been noted that cavity searches for interactions between photons and exotic fields may also…
We uncover a strong coupling between nonlinearity and diffraction in a photonic crystal at the supercollimation point. We show this is modeled by a nonlinear diffraction term in a nonlinear schroedinger type equation, in which the…
The soliton effect is defined in nonlinear physics by the transformation of a nonlinear time-dependent dynamical system into an equivalent linear spectral eigenproblem whose invariant eigenvalues unambiguously define all the dynamical…
We study the dynamics of solitons under the action of one-dimensional quasiperiodic lattice potentials, fractional diffraction, and nonlinearity. The formation and stability of the solitons is investigated in the framework of the fractional…
We introduce a generalized version of the Ablowitz-Ladik model with a power-law nonlinearity, as a discretization of the continuum nonlinear Schr\"{o}dinger equation with the same type of the nonlinearity. The model opens a way to study the…
In a recent one-dimensional numerical fluid simulation study [Saxena et al., Phys. Plasmas 13,032309 (2006)], it was found that an instability is associated with a special class of one-dimensional nonlinear solutions for modulated light…
A model including two nonlinear chains with linear and nonlinear couplings between them, and opposite signs of the discrete diffraction inside the chains, is introduced. For [$\chi ^{(3)}$] nonlinearity, the model finds two different…
The understanding and prediction of sudden changes in flow patterns is of paramount importance in the analysis of geophysical flows as these rare events relate to critical phenomena such as atmospheric blocking, the weakening of the Gulf…
We revisit the mechanisms underlying the process of spectral broadening of incoherent optical waves propagating in nonlinear media on the basis of nonequilibrium thermodynamic considerations. A simple analysis reveals that a prerequisite…
We study bifurcations and spectral stability of solitary waves in coupled nonlinear Schr\"odinger equations (CNLS) on the line. We assume that the coupled equations possess a solution of which one component is identically zero, and call it…
We report a new type of symmetry-breaking bifurcation of solitons in optical systems with parity-time-symmetric potentials. In this bifurcation, the two bifurcated branches of asymmetric solitons exhibit opposite stability, which contrasts…
Self-organization is the spontaneous formation of spatial, temporal, or spatiotemporal patterns in complex systems far from equilibrium. During such self-organization, energy distributed in a broadband of frequencies gets condensed into a…
We study the instability of the spectrum for a class of non-selfadjoint anharmonic oscillators, estimating the behavior of the instability indices (i. e. the norm of spectral projections) associated with the large eigenvalues of these…
Understanding, predicting, and controlling physical processes often relies on the analysis of the dynamics of partial differential equations (PDEs). In this context, the present study offers an in-depth investigation into the nonlinear…
We consider the spectrum of BPS saturated states in $N = 2$ gauge theories in four dimensions. This spectrum may be discontinuous across real codimension one submanifolds of marginal stability in the moduli space of vacua. An example, which…
Nonlinear wave interactions affect the evolution of steep wave groups, their breaking and the associated kinematic field. Laboratory experiments are performed to investigate the effect of the underlying focussing mechanism on the shape of…
It is commonly held that a necessary condition for the existence of solitons in nonlinear-wave systems is that the soliton's frequency (spatial or temporal) must not fall into the continuous spectrum of radiation modes. However, this is not…
We report analytical solutions for spatial solitons supported by layers of a quadratically nonlinear material embedded into a linear planar waveguide. A full set of symmetric, asymmetric, and antisymmetric modes pinned to a symmetric pair…
Systems that are not smooth can undergo bifurcations that are forbidden in smooth systems. We review some of the phenomena that can occur for piecewise-smooth, continuous maps and flows when a fixed point or an equilibrium collides with a…