The Kadomtsev-Petviashvili II (KPII) equation admits a large variety of multi-soliton solutions which exhibit both elastic as well as inelastic types of interactions. This work investigates a general class of multi-solitons which were not previously studied, and which do not in general conserve the number of line solitons after interaction. The incoming and outgoing line solitons for these solu...

The existence of ring-like and knotted solitons in O(3) non-linear σ model is analysed. The role of isotopy of knots/links in classifying such solitons is pointed out. Appearance of torus knot solitons is seen. †[email protected]; [email protected] †† permanent address Introduction: Recently the possible existence of knotlike solitons in nonlinear field theories has been argued[1, 2]. ...

The redistribution of conserved quantities among colliding solitons of the nonlinear Schrödinger equation is considered. An analogy with the theory of spatial solitons in nonlinear optics provides one way to calculate this redistribution. In this context, exchanges of conserved quantities among N colliding solitons can be completely described from a knowledge of the case for N ­ 2. It is shown ...

We experimentally investigate the interaction of counterpropagating discrete solitons in a one-dimensional waveguide array in photorefractive lithium niobate. While for low input powers only weak interaction and formation of counterpropagating vector solitons are observed, for higher input powers a growing instability results in discrete lateral shifting of the formed discrete solitons. Numeric...

Many physical phenomena are modeled with nonlinear partial differential equations that possess solitary wave solutions called solitons. Solitons exhibit Gaussian forms and in turn engender normal probability distributions. Moreover, solitons fluctuate randomly during evolution. These features intricately relate the solitons to wavelets, statistical distributions and random processes. In the pre...

We report on the formation and stability of induced solitons in parity-time (PT) symmetric periodic systems with the logarithmically saturable nonlinearity. Both on-site and off-site lattice solitons exist for the self-focusing nonlinearity. The most intriguing result is that the above solitons can also be realized inside the several higher-order bands of the band structure, due to the change o...

We show that the quadratic interaction of fundamental and second harmonics in a bulk dispersive medium, combined with self-defocusing cubic nonlinearity, gives rise to completely localized spatiotemporal solitons (vortex tori) with vorticity s=1. There is no threshold necessary for the existence of these solitons. They are found to be stable if their energy exceeds a certain critical value, so ...

We consider solutions to the second-harmonic generation equations in twoand three-dimensional dispersive media in the form of solitons localized in space and time. As is known, collapse does not take place in these models, which is why the solitons may be stable. The general solution is obtained in an approximate analytical form by means of a variational approach, which also allows the stabilit...

We develop a general theory of spatial solitons in a liquid crystalline medium exhibiting a nonlinearity with an arbitrary degree of effective nonlocality. The model accounts the observability of accessible solitons and establishes an important link with parametric solitons.

In this paper we extend existing results for generalized solitons, called $q$-solitons, to the complete case by considering non-compact solitons. By placing regularity conditions on vector field $X$ and curvature $M$, are able use chosen properties of tensor $q$ see that such $q$-solitons stationary $q$-flat. We conclude applying our examples ambient obstruction Cotton Bach solitons demonstrate...