Eur. Phys. J. Special Topics 227, 551–561 (2018)
https://doi.org/10.1140/epjst/e2018-00118-5

Regular Article

Influence of pseudo-stimulated-Raman-scattering on the modulational instability in an inhomogeneous nonlinear medium

¹ Instituto de Física, Universidade Federal de Goiás, 74.690-900, Goiânia, Goiás, Brazil
² Instituto Federal de Goiás, 74.968-755, Aparecida de Goiânia, Goiás, Brazil
³ Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978, Israel
⁴ ITMO University, St. Petersburg 197101, Russia

^a e-mail: wesleybcardoso@gmail.com

Received: 11 November 2017
Received in final form: 22 January 2018
Published online: 4 October 2018

Abstract

We study the influence of the pseudo-Raman effect on the modulation instability (MI) in an inhomogeneous nonlinear medium. The system is governed by the extended nonlinear Schrödinger (NLS) equation, which is derived from a Zakharov-type system for the interaction between high-frequency and low-frequency waves. The resulting inhomogeneous NLS equation includes a pseudo-stimulated-Raman-scattering term. The model may apply to the propagation of waves in plasmas, surface waves in the ocean, and optical beams in nonlinear waveguides. This nonautonomous model is converted into an autonomous equation by a similarity transformation, allowing us to find MI regions of the system. The results suggest new possibilities for controlling multi-soliton patterns generated by the MI. The MI patterns are also produced by numerical simulations that confirm the analytical results.