We describe basic features of multisoliton collisions in nearly integrable systems taking a perturbed nonlinear Schrödinger equation as an example. Collision of two solitons is shown to become inelastic only due to radiation losses, so that the change of the soliton parameters is small (;e, where e is the perturbation amplitude!. For three-soliton collisions we demonstrate, by using a simplecti...

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A model of soliton-defect interactions in the sine-Gordon equations is studied using singular perturbation theory. Melnikov theory is used to derive a critical velocity for strong interactions, which is shown to be exponentially small for weak defects. Matched asymptotic expansions for nearly heteroclinic orbits are constructed for the initial value problem, which are then used to derive analyt...

We use the Riemann-Hilbert problem to study the interaction of the soliton with radiation in the parametrically driven, damped nonlinear Schrödinger equation. The analysis is reduced to the study of a finite-dimensional dynamical system for the amplitude and phase of the soliton and the complex amplitude of the long-wavelength radiation. In contrast to previously utilised Inverse Scattering-bas...

The Riemann-Hilbert problem associated with the integrable PDE is used as a nonlinear transformation of the nearly integrable PDE to the spectral space. The temporal evolution of the spectral data is derived with account for arbitrary perturbations and is given in the form of exact equations, which generate the sequence of approximate ODEs in successive orders with respect to the perturbation. ...

We search for a possible bosonic (i.e. non-supersymmetric) string/gauge theory correspondence by using ten-dimensional IIB and 0B strings as a guide. Our construction is based on the low-energy bosonic string effective action modified by an extra form flux. The closed string tachyon can be stabilyzed if the AdS scale L does not exceed certain critical value, L < L c. We argue that the extra for...