We predict the existence of multifrequency gap solitons (MFGSs) in both one- and two-dimensional nonlinear photonic crystals. A MFGS is a single intrinsic mode possessing multiple frequencies inside the gap. Its existence is a result of synergic nonlinear coupling among solitons or soliton trains at different frequencies. Its formation can either lower the threshold fields of the respective fre...

Stable embedded solitons are discovered in the generalized third-order nonlinear Schrödinger equation. When this equation can be reduced to a perturbed complex modified Korteweg-de Vries equation, we developed a soliton perturbation theory which shows that a continuous family of sech-shaped embedded solitons exist and are nonlinearly stable. These analytical results are confirmed by our numeric...

We develop a theory of modulational instability of multiparameter solitary waves and analyze the transverse instability of composite (or vector) optical solitons in a saturable nonlinear medium. We demonstrate theoretically and experimentally that a soliton stripe breaks up into an array of ( 2+1)-dimensional dipole-mode vector solitons, thus confirming the robust nature of those solitons as fu...

We study solitons in one-dimensional quadratic nonlinear photonic crystals with modulation of both the linear and nonlinear susceptibilities. We derive averaged equations that include induced cubic nonlinearities, which can be defocusing, and we numerically find previously unknown soliton families. Because of these induced cubic terms, solitons still exist even when the effective quadratic nonl...

We consider the averaged dispersion-managed (DM) fiber system equation, which governs the dynamics of the core of the DM solitons. For a special case of such a system equation, we derive the exact soliton solutions using the Darboux transformation. Further, we discuss the interaction scenario between two neighboring solitons. Finally, we derive a dark soliton solution for such a system by assum...

We describe different types of ring-profile optical solitary wave and clusters of fundamental solitons propagating in isotropic nonlinear optical media. Such ringlike solitons carry a finite angular momentum and, depending on the value of the total momentum and structure, they either fragment quickly into several fundamental solitons that fly off the ring, or propagate stably for many diffracti...

A class of optical spatial solitons exhibiting propagation in a closed-loop orbit in a two-dimensional plane is presented. A closed-form particlelike model is derived, indicating that the quasi-centrifugal force acting on these solitons can be balanced by an inhomogeneity in the nonlinear index of refraction. Specifically, a circular-shaped nonlinear interface is shown to facilitate stable orbi...

We discover multipole-mode solitons supported by the surface between two distinct periodic lattices imprinted in Kerr-type nonlinear media. Such solitons are possible because the refractive index modulation at both sides of the interface glues together their out-of-phase individual constituents. Remarkably, we find that the new type of solitons may feature highly asymmetric shapes, and yet they...

Using methods of high performance computing, we have found indications that knotlike structures appear as stable finite energy solitons in a realistic 3+1 dimensional model. We have explicitly simulated the unknot and trefoil configurations, and our results suggest that all torus knots appear as solitons. Our observations open new theoretical possibilities in scenarios where stringlike structur...

We give a classical geometric optics description of incoherent solitons—those launched by a diffuse source. This method is intuitive, advances predictions such as the existence of solitons of arbitrary cross section, and importantly, it provides a simple (universal) analytical description for the incoherent solitons of any nonlinear medium. Previously, analytical results were known for the ln I...