相关论文: Stability of multi-hump optical solitons
We consider the stability problem for standing waves of nonlinear Dirac models. Under a suitable definition of linear stability, and under some restriction on the spectrum, we prove at the same time orbital and asymptotic stability. We are…
We demonstrate that matter-wave bright solitons can be stabilized in 2D free space by causing the strength of interactions to oscillate rapidly between repulsive and attractive by using, e.g., Feshbach resonance.
This paper explores the analytical approach for obtaining the multiple solutions of three-wave interacting system in (1+1) dimensions. We present a novel approach by expressing the wave solutions in terms of Jacobi elliptic functions and…
Stable embedded solitons are discovered in the generalized third-order nonlinear Schroedinger equation. When this equation can be reduced to a perturbed complex modified KdV equation, we developed a soliton perturbation theory which shows…
Beam stability and halo formation in high-intensity axisymmetric 2D beams in a uniform focusing channel are analyzed using particle-in-cell simulations. The tune depression - mismatch space is explored for the uniform (KV) distribution of…
General asymptotic approach to the stability problem of multi-parameter solitons in Hamiltonian systems $i\partial E_n/\partial z=\delta H/\delta E_n^*$ has been developed. It has been shown that asymptotic study of the soliton stability…
Coulomb bubbles, though stable against monopole displacement, are unstable at least with respect to quadrupole and octupole distortions. We show that there exists a temperature at which the pressure of the vapor filling the bubble…
The $b$-family of Camassa-Holm ($b$-CH) equation is a one-parameter family of PDEs, which includes the completely integrable Camassa-Holm and Degasperis-Procesi equations but possesses different Hamiltonian structures. Motivated by this, we…
We examine the dynamics of a bright solitary wave in the presence of a repulsive or attractive localized ``impurity'' in Bose-Einstein condensates (BECs). We study the generation and stability of a pair of steady states in the vicinity of…
We present the first experimental observation of modulation instability of partially spatially incoherent light beams in non-instantaneous nonlinear media. We show that even in such a nonlinear partially coherent system (of…
We study the notion of stochastic stability with respect to diffusive perturbations for flows with smooth invariant measures. We investigate the question fully for non-singular flows on the circle. We also show that volume-preserving flows…
Early results concerning the shape and stability of ion acoustic waves are generalized to propagation at an angle to the magnetic field lines. Each wave has a critical angle for stability. Known soliton results are recovered as special…
We consider the linear stability of chiral matter-wave solitons described by a density-dependent gauge theory. By studying the associated Bogoliubov-de Gennes equations both numerically and analytically, we find that the stability problem…
We report on the existence and stability of multicolor lattice vortex solitons constituted by coupled fundamental frequency and second-harmonic waves in optical lattices in quadratic nonlinear media. It is shown that the solitons are stable…
We study the behavior of nonlinear waves in a two-dimensional medium with density and stress relation that vary periodically in space. Efficient approximate Riemann solvers are developed for the corresponding variable-coefficient…
We consider the propagation of smooth solitary waves in a two-dimensional generalization of the Camassa--Holm equation. We show that transverse perturbations to one-dimensional solitary waves behave similarly to the KP-II theory. This…
Optomechanical manipulation of nanoparticles enabling ultimate control over their 3D motion is nowadays one of the most highly demanded links between optics, biology, medicine, microfluidics, etc., paving the way for a plethora of emerging…
Solitons are non-dispersive wave solutions that arise in a diverse range of nonlinear systems, stablised by a focussing or defocussing nonlinearity. First observed in shallow water, solitons have subsequently been studied in many other…
This is the second paper in a series studying the nonlinear stability of rarefaction waves in multi-dimensional gas dynamics. We construct initial data near singularities in the rarefaction wave region and, combined with the a priori energy…
We have found various families of two-dimensional spatiotemporal solitons in quadratically nonlinear waveguide arrays. The families of unstaggered odd, even and twisted stationary solutions are thoroughly characterized and their stability…