parameterized by θ ∈ R. But we do not expect that the “sum” of two such solutions will again be a solution. However, the special class of soliton equations, the subject of this article, does have a form of nonlinear superposition. An n-soliton solution is a solution that is asymptotic to a nontrivial sum of n solitary waves ∑n i=1 fi(x− cit) as t → −∞ and to the sum of the same waves ∑n i=1 fi(...

A dispersion-managed optical system with stepwise periodic variation of dispersion is studied in a strong dispersion map limit in the framework of the path-averaged Gabitov-Turitsyn equation. The soliton solution is obtained by analytical and numerical iteration of the path-averaged equation. An efficient numerical algorithm for finding a DM soliton shape is developed. The envelope of soliton o...

We present a simple approach for finding N -soliton solution and the corresponding Jost solutions of the derivative nonlinear Scrödinger equation with nonvanishing boundary conditions. Soliton perturbation theory based on the inverse scattering transform method is developed. As an application of the present theory we consider the action of the diffusive-type perturbation on a single bright/dark...

We consider world-volume description of M2-branes ending on an M5-brane. The system can be described either as a solitonic solution of the M5-brane field equations or in terms of an effective string propagating in 6-dimensions. We show that the zeroth order scalar scattering amplitudes behave similarly in both pictures. The soliton solution appears to have a horizon-like throat region. Due to t...

A different kind of shape changing (intensity redistribution) collision with potential application to signal amplification is identified in the integrable -coupled nonlinear Schrödinger (CNLS) equations with mixed signs of focusing- and defocusing-type nonlinearity coefficients. The corresponding soliton solutions for the N=2 case are obtained by using Hirota's bilinearization method. The disti...

The paper deals with the Korteweg-de Vries equation variable coefficients and a small parameter at highest derivative. non-linear WKB technique has been used to construct asymptotic step-like solution equation. Such contains regular singular parts of asymptotics. part describes background wave process, while its reflects specific features associated soliton properties. searched asymp\-totic mai...

We consider a simple SU(2) quark soliton model based on chiral invariant quark-meson couplings. We nd axially symmetric, classically stable soliton solutions with B=2,3 and 4 (where B is the baryon number). The energy distributions corresponding to these solutions are toroidal in nature. The symmetries of the B=2 solution indicate that the ground state of this solution has the quantum numbers o...

Solitons are wave phenomena or pulses that can maintain their shape stability when propagating in a medium. In optical fibers, they become general solutions of the Non-Linear Schrödinger Equation (NLSE). Despite its mathematical complexity, NLSE has been an interesting issue. Soliton analysis and techniques to solve problems equation keep doing. Yan Chen (2022) introduced them based on bilinear...

The Painlevé integrability of the 2+1 dimensional AKNS system is proved. Using the standard truncated Painlevé expansion which corresponds to a special Bäcklund transformation, some special types of the localized excitations like the solitoff solutions, multi-dromion solutions and multi-ring soliton solutions are obtained. PACS. 02.30.Ik Integrable systems – 02.30.Jr Partial differential equati...

We study the properties of soliton solutions in an analog of the Skyrme model in 2+1 dimensions whose Lagrangian contains the Skyrme term and the mass term, but no usual kinetic term. The model admits a symmetry under area preserving diffeomorphisms. We solve the dynamical equations of motion analytically for the case of spinning isolated baryon type solitons. We take fully into account the ind...