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{\Large\bf Resonant control of solitons}

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S.V. Batalov, A.G. Shagalov

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{\it Institute of Metal Physics, S.Kovalevskaya 18, Ekaterinburg 620990, Russian Federation.
E-mail: shagalov@imp.uran.ru}
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Control of envelope solitons and, in particular, amplification of solitons, is a fundamental problem
in nonlinear optics, spin waves in magnetics and another applications in
condensed matter physics.

An effective method to excite and control envelope solitons was proposed in Refs.[1,2].
The method was based on
the autoresonant phenomenon when the soliton was captured by the resonant driving with the frequency
close to the internal frequency of the soliton.
However, the method appears very difficult for applications because the capture of the soliton of a finite amplitude
occurs only in a narrow range of the driving frequencies and with strong restrictions on the phase of the
driving. In this paper we propose that, in contrast to the autoresonance, the promising method of
control and amplification of solitons can be based on the "scattering on resonance" [3,4] without capture of the soliton. The control occurs by the frequency
modulated driving with multiple crossing of the resonant frequency of the soliton [5].
The proposed method overcomes strong restrictions on the driving which are required to control solitons
in the autoresonant approach.

The research was supported by UD RAS, project No 12-P-2-1045.


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[1] L. Friedland, A.G. Shagalov, Phys. Rev. E {\bf 71}, 036206 (2005).

[2] S. V. Batalov, E. M. Maslov, A. G. Shagalov, Zh. Eksp. Teor. Fiz. {\bf 108}, 1021 (2009)
[ Sov. Phys. JETP {\bf 108}, 890 (2009)].

[3] B.V. Chirikov, Dokl. Akad. Nauk SSSR {\bf 125}, 1015 (1959) [Sov. Phys. Dokl. {\bf 4}, 400 (1959)].

[4] A.I. Neishtadt, in {\it Proceedings of the Steklov Institute of Mathematics}, {\bf 250}, 183 (2005).

[5] S. V. Batalov, A. G. Shagalov, Phys.Lett. A {\bf 377}, 964 (2013).

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