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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. [ABSTRACT FROM AUTHOR]

Abstract: One‐dimensional nonlinear Schrödinger equations are derived to describe the axial effective dynamics of cigar‐shaped atomic repulsive Bose‐Einstein condensates trapped with anharmonic transverse potentials. The accuracy of these equations in the perturbative, Thomas‐Fermi, and crossover regimes were verified numerically by comparing the ground‐state profiles, transverse chemical potentials and oscillation patterns with those results obtained for the full three‐dimensional Gross‐Pitaevskii equation. This procedure allows us to derive different patterns of 1D nonlinear models by the control of the transverse confinement even in the presence of an axial vorticity. [ABSTRACT FROM AUTHOR]