Cubic-quintic nonlinear Helmholtz equation: Modulational instability, chirped elliptic and solitary waves

DOI10.1063/1.5096844zbMath1421.35344arXiv1906.02908OpenAlexW2948659765WikidataQ91559780 ScholiaQ91559780MaRDI QIDQ5227590

T. Kanna, A. Govindarajan, K. Tamilselvan

Publication date: 6 August 2019

Published in: Chaos: An Interdisciplinary Journal of Nonlinear Science (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1906.02908

zbMATH Keywords

nonlinear Schrödinger systemplanar waveguidecubic-quintic nonlinear Helmholtz equationchirped elliptic and solitary wavesKerr-like and quintic nonlinearities

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Antennas, waveguides in optics and electromagnetic theory (78A50) Lasers, masers, optical bistability, nonlinear optics (78A60) Soliton solutions (35C08)

Related Items (5)

Construction of the soliton solutions and modulation instability analysis for the Mel'nikov system ⋮ Computing solitary wave solutions of coupled nonlinear Hirota and Helmholtz equations ⋮ Detailed analysis for chirped pulses to cubic-quintic nonlinear non-paraxial pulse propagation model ⋮ On the integrability aspects of nonparaxial nonlinear Schrödinger equation and the dynamics of solitary waves ⋮ Reviving modulational instability with third-order dispersion

Cites Work

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• A split-step finite difference method for nonparaxial nonlinear Schrödinger equation at critical dimension
• Modulation instability and periodic solutions of the nonlinear Schrödinger equation
• Stability of the soliton-like ``bubbles
• Stability and evolution of the quiescent and travelling solitonic bubbles
• Nonparaxial elliptic waves and solitary waves in coupled nonlinear Helmholtz equations
• Lie symmetry analysis and group invariant solutions of the nonlinear Helmholtz equation
• Nonparaxial one-dimensional spatial solitons

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