We study the magnon modes in the presence of a topological soliton in a two-dimensional Heisenberg easy-axis ferromagnet. The problem of magnon scattering on the soliton with arbitrary relation between the soliton radius R and the ‘‘magnetic length’’ D0 is investigated for partial modes with different values of the azimuthal quantum numbers m. Truly local modes are shown to be present for all v...

An explicit two-soliton solution for the derivative nonlinear Schrödinger equation with nonvanishing boundary conditions is derived, demonstrating details of interactions between two bright solitons, two dark solitons, as well as one bright soliton and one dark soliton. Shifts of soliton positions due to collisions are analytically obtained, which are irrespective of the bright or dark characte...

Based on the factorization of soliton equations into two commuting integrable xand t-constrained flows, we derive N -soliton solutions for mKdV equation via its xand t-constrained flows. It shows that soliton solution for soliton equations can be constructed directly from the constrained flows.

Introduction.– Many nonlinear classical field theories on flat spacetime backgrounds admit soliton solutions. These nonsingular solutions describe particle-like, localised configurations with finite energy. There has been some interest in recent years in the issue of globally regular spinning soliton solutions. However, to the best of our knowledge, to date no static and stable spinning soliton...

We study the soliton type solutions arising in two-dimensional quantum chromodynamics (QCD2). In bosonized QCD2 these type of solutions emerge as describing baryons and quark solitons (excitations with “colored” states), respectively. The so-called generalized sine-Gordon model (GSG) arises as the low-energy effective action of bosonized QCD2 for unequal quark mass parameters, and it has been s...

We derive the Kadomtsev-Petviashvili (KP) equation defined over a general associative algebra and construct its N -soliton solution. For the example of the Moyal algebra, we find multi-soliton solutions for arbitrary space-space noncommutativity. The noncommutativity of coordinates is shown to obstruct the general construction of a τ function for these solitons. We investigate the two-soliton s...

We use the physics-informed neural network to solve a variety of femtosecond optical soliton solutions high-order nonlinear Schrödinger equation, including one-soliton solution, two-soliton rogue wave W-soliton solution and M-soliton solution. The prediction error for one-soliton, is smaller. As distance increases, will gradually increase. unknown physical parameters equation are studied by usi...

The adiabatic parameter dynamics of 1-soliton solution of the generalized fifth-order nonlinear equation is obtained by virtue of the soliton perturbation theory. The adiabatic change of soliton velocity is also obtained in this paper.

In this paper, we construct the Lax pair for a soliton transmission system in nonuniform optical fibers and give N-soliton solution using the Darboux transformation. The explicit one-soliton and two-soliton solutions are presented. Further, we discuss the interaction scenario between two neighboring solitons and the effect of the inhomogeneities of the fiber (z0) on the interaction between two ...

A variational method is used to obtain the growth rate of a transverse long-wavelength perturbation applied to the soliton solution of a nonlinear Schrödinger equation with a three-half order potential. We demonstrate numerically that this unstable perturbed soliton will eventually transform into a cylindrical soliton. Keywords—soliton, instability, variational method, spectral method