Using the nonlinear constraint and Darboux transformation methods, the (m1, · · · ,mN ) localized solitons of the hyperbolic su(N) AKNS system are constructed. Here “hyperbolic su(N)” means that the first part of the Lax pair is Ψy = JΨx + U(x, y, t)Ψ where J is constant real diagonal and U = −U . When different solitons move in different velocities, each component Uij of the solution U has at ...

We predict that strong coupling between waveguide photons and excitons of quantum well embedded into waveguide results in the formation of hybrid-dark and antidark light-matter solitons. Such temporal solitons exist due to interplay between repulsive excitonic nonlinearity and giant group-velocity dispersion arising in the vicinity of excitonic resonance. Such fully conservative states do not r...

We study propagation of solitons in optical fibers with randomly varying birefringence which results in polarization mode dispersion. Due to the disorder, solitons emit radiation, i.e., the energy of the solitons is partly transferred into the delocalized modes. The radiation serves as a mediator of the intersoliton interaction leading to fluctuations of the soliton separations. We establish st...

Sources of photons with controllable quantum properties such as entanglement and squeezing are desired for applications in information, metrology, sensing. However, fine-grained control over these is hard to achieve, especially two-photon sources. Here, we propose a new mechanism generating entangled squeezed photon pairs using superluminal and/or accelerating modulations the refractive index m...

‎we study curvature properties of four-dimensional lorentzian manifolds with two-symmetry property‎. ‎we then consider einstein-like metrics‎, ‎ricci solitons and homogeneity over these spaces‎‎.

We introduce the concept of this special focus issue on solitons in nonintegrable systems. A brief overview of some recent developments is provided, and the various contributions are described. The topics covered in this focus issue are the modulation of solitons, bores, and shocks, the dynamical evolution of solitary waves, and existence and stability of solitary waves and embedded solitons.

In this paper, we prove the asymptotic stability of the family of solitons of the Benjamin-Ono equation in the energy space. The proof is based on a Liouville property for solutions close to the solitons for this equation, in the spirit of [16], [18]. As a corollary of the proofs, we obtain the asymptotic stability of exact multi-solitons.

We address the stability of multipole-mode solitons in nonlocal Kerr-type nonlinear media. Such solitons comprise several out-of-phase peaks packed together by the forces acting between them. We discover that dipole-, triple-, and quadrupole-mode solitons can be made stable, whereas all higher-order soliton bound states are unstable.

Using an example of cavity solitons in optical parametric oscillators it is demonstrated that Hopf instability of these dissipative structures can be directly associated with internal modes of their conservative counterparts. The latter ones are free propagating quadratic solitons in this case. Linear stability analysis and numerical simulation also reveal multistability and complex instability...

We define a gradient Ricci soliton to be rigid if it is a flat bundle N×ΓR k where N is Einstein. It is known that not all gradient solitons are rigid. Here we offer several natural conditions on the curvature that characterize rigid gradient solitons. Other related results on rigidity of Ricci solitons are also explained in the last section.