Emulating the Raman Physics in the Spatial Domain with the Help of the Zakharov’s Systems

  • Evgeny M. GromovEmail author
  • Boris A. Malomed
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 90)


Dynamics of solitons is considered in the framework of the extended nonlinear Schrödinger equation (NLSE), which is derived from a system of the Zakharov’s type for the interaction between high- and low-frequency (HF and LF) waves, in which the LF field is subject to diffusive damping. The model may apply to the propagation of HF waves in plasmas. The resulting NLSE includes a pseudo-stimulated-Raman-scattering (pseudo-SRS) term, i.e., a spatial-domain counterpart of the SRS term which is well known as an ingredient of the temporal-domain NLSE in optics. Also included is inhomogeneity of the spatial second-order diffraction (SOD). It is shown that the wavenumber downshift of solitons, caused by the pseudo-SRS, may be compensated by an upshift provided by the SOD whose coefficient is a linear function of the coordinate. An analytical solution for solitons is obtained in an approximate form. Analytical and numerical results agree well, including the predicted balance between the pseudo-SRS and the linearly inhomogeneous SOD.



The work of B.A.M. is supported, in part, by grant No. 2015616 from the joint program in physics between National Science Foundation (US) and Binational (US-Israel) Science Foundation, and by grant No. 1287/17 from the Israel Science Foundation.


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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.National Research University Higher School of EconomicsNizhny NovgorodRussia
  2. 2.Faculty of Engineering, Department of Physical ElectronicsTel Aviv UniversityTel AvivIsrael
  3. 3.ITMO UniversitySt. PetersburgRussia

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