Vsevolod V. Afanasjev

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Time-localized solitary wave solutions of the one-dimensional complex Ginzburg-Landau equation ͑CGLE͒ are analyzed for the case of normal group-velocity dispersion. Exact soliton solutions are found for both the cubic and the quintic CGLE. The stability of these solutions is investigated numerically. The regions in the parameter space in which stable(More)
Nonlinear theory describing the instability-induced dynamics of dark solitons in the generalized nonlinear Schrödinger equation is presented. Equations for the evolution of an unstable dark soliton, including its transformation into a stable soliton, are derived using a multiscale asymptotic technique valid near the soliton instability threshold. Results of(More)
It is shown that self-guided optical beams with power-law asymptotics, i.e., algebraic optical solitons, can be regarded as a special case of sech-type solitons ͑i.e. solitons with exponentially decaying asymptotics͒ in the limit where the beam propagation constant coincides with the threshold for linear wave propagation. This leads to the conjecture that(More)
The concept of soliton internal mode is introduced to explain quantitatively the long-lived oscillations of self-guided beams, or breathing spatial solitons. Cubic-quintic nonlinearity is considered in detail, and it is shown that the existence of the internal mode affects strongly the beam propagation in non-Kerr media, leading to oscillatory dependence of(More)
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