Adiabatic evolution equations for parameters of the perturbed DNLS/MNLS solitons obtained by recently developed direct perturbation theory [X.-J. Chen and J. Yang, Phys. Rev. E 65, 066608(2002)] are reformulated in simpler forms for practical use. A symbolic computation technique is developed to calculate them, based on the residue theorem. Effects of the third-order dispersion on the MNLS soli...

We study fully localized BPS brane solutions in classical supergravity using a perturbative approach to the coupled Born-Infeld/bulk supergravity system. We derive first order bulk supergravity fields for world-volume solitons corresponding to intersecting M2branes and to a fundamental string ending on a D3-brane. One interesting feature is the appearance of certain off-diagonal metric componen...

We integrate the one-dimensional nonlinear Schrr odinger equation numerically for solitons moving in external potentials. In particular, we study the scattering oo an interface separating two regions of constant potential modeled by a linear ramp. Transmission coeecients and inelasticities are computed as functions of the potential diierence and the slope of the ramp. Our data show that the ram...

A detailed survey of the technique of perturbation theory for nearly integrable systems, based upon the inverse scattering transform, and a minute account of results obtained by means of that technique and alternative methods are given. Attention is focused on four classical nonlinear equations: the Korteweg —de Vries, nonlinear Schrodinger, sine-Gordon, and Landau-Lifshitz equations perturbed ...

We consider in detail the self-trapping of a soliton from a wave pulse that passes from a defocusing region into a focusing one in a spatially inhomogeneous nonlinear waveguide, described by a nonlinear Schrodinger equation in which the dispersion coefficient changes its sign from normal to anomalous. The model has direct applications to dispersion-decreasing nonlinear optical fibers, and to na...

Self-gravitating quantum matter may exist in a wide range of cosmological and astrophysical settings from the very early universe through to present-day boson stars. Such arises number different theories, including Peccei-Quinn axion UltraLight (ULDM) or Fuzzy (FDM) dark scenarios. We consider dynamical evolution perturbations spherically symmetric soliton, ground state solution Schr\"{o}dinger...

We consider the collision of a dark soliton with an obstacle in a quasi one dimensional Bose condensate. The variation of the soliton’s shape and velocity during the collision are first determined within the adiabatic approach. In this framework, an “effective potential approximation” is established where the soliton behaves as an effective classical particle of mass twice the mass of a bare pa...

The variational principle is employed to obtain the parameters dynamics of Gaussian and super-Gaussian chirped solitons which propagates through birefringent optical fibers that is governed by the dispersion-managed vector nonlinear Schrödinger’s equation. The waveform deviates from that of a classical soliton. The periodically changing strong chirp of such a soliton reduces the effective nonli...

A direct approach is applied to the periodic amplification of a soliton in an optical fibre link with loss. In a single soliton case, the adiabatic solution and first-order correction are given for the system. The apparent advantage of this direct approach is that it not only presents the slow evolution of soliton parameters, but also the perturbation-induced radiation, and can be easily used t...

daisuke takahashi waseda univ " ultradiscretization method " found in the area of soliton theory introduction to soliton (integrable) equations N soliton solution, infinite number of conserved quantities, bilinear form, inverse scattering method, Lax form, Sato theory