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V. S. Shchesnovich

Publications and source records attributed to V. S. Shchesnovich.

42 records · Page 3Linked to original sources
arXiv2001

Perturbation theory for nearly integrable multi-component nonlinear PDEs

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. For vector nearly integrable PDEs, embracing the vector NLS and complex modified KdV equations, the main result is formulated in a theorem. For a single vector soliton the evolution equations for the soliton parameters and first-order radiation are given in explicit form

nlin.SI↗
arXiv2001

Interaction of N solitons in the massive Thirring model and optical gap system: the Complex Toda Chain Model

Using the Karpman-Solov''ev quasiparticle approach for soliton-soliton interaction I show that the train propagation of N well separated solitons of the massive Thirring model is described by the complex Toda chain with N nodes. For the optical gap system a generalised (non-integrable) complex Toda chain is derived for description of the train propagation of well separated gap solitons. These results are in favor of the recently proposed conjecture of universality of the complex Toda chain.

nlin.SI↗
arXiv2000

Nearly integrable nonlinear equations on the half line

We employ the Riemann-Hilbert problem for solution of the initial-boundary value problems for nearly integrable equations on the half line which have important applications in physics. The detailed derivation of the integrable and perturbation-induced evolutions of the spectral data are given for the two most important models, the self-induced transparency and the stimulated Raman scattering. In particular, we prove that dephasing stabilizes the spike phenomenon in the stimulated Raman scattering.

nlin.SI↗
arXiv1998

Perturbation theory for the modified nonlinear Schr{ö}dinger solitons

The perturbation theory based on the Riemann-Hilbert problem is developed for the modified nonlinear Schr{ö}dinger equation which describes the propagation of femtosecond optical pulses in nonlinear single-mode optical fibers. A detailed analysis of the adiabatic approximation to perturbation-induced evolution of the soliton parameters is given. The linear perturbation and the Raman gain are considered as examples.

solv-int↗