Generalized Models and Non-classical Approaches in Complex Materials 2. Advanced Structured Materials

Springer, 2018.

Academic editor: H. Altenbach, J. Pouget, M. Rousseau, B. Collet

Dynamics of solitons is considered in the framework of the extended nonlinear Schrödinger equation (NLSE), which is derived from a system of 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

Chapters

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

Gromov E., Malomed B., , in: Generalized Models and Non-classical Approaches in Complex Materials 2. Advanced Structured Materials.: Springer, 2018. Ch. 6 P. 119–144.

Dynamics of solitons is considered in the framework of the extended nonlinear Schrödinger equation (NLSE), which is derived from a system of 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 ...

Added: July 19, 2018

Keywords: расширенное нелинейное уравнение Шредингера, Extended Nonlinear Schrödinger Equation