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Embedded solitons with χ(2) and χ(3) nonlinear susceptibilities having multiplicative white noise via Itô Calculus

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  • Zayed, Elsayed M.E.
  • Alngar, Mohamed E.M.
  • Shohib, Reham M.A.
  • Biswas, Anjan
  • Yıldırım, Yakup
  • Moraru, Luminita
  • Mereuta, Elena
  • Alshehri, Hashim M.

Abstract

The objective of this paper is to locate the embedded solitons with χ(2) and χ(3) nonlinear susceptibilities in presence of multiplicative noise. Itô Calculus was implemented to carry out the analysis of the corresponding stochastic differential equation. The unified Riccati equation expansion method and enhanced Kudryashov’s approach yielded dark, bright and singular solitons. The derived soliton solutions show that the effect of white noise is present only in the phase component.

Suggested Citation

  • Zayed, Elsayed M.E. & Alngar, Mohamed E.M. & Shohib, Reham M.A. & Biswas, Anjan & Yıldırım, Yakup & Moraru, Luminita & Mereuta, Elena & Alshehri, Hashim M., 2022. "Embedded solitons with χ(2) and χ(3) nonlinear susceptibilities having multiplicative white noise via Itô Calculus," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    • Handle: RePEc:eee:chsofr:v:162:y:2022:i:c:s0960077922007007
    DOI: 10.1016/j.chaos.2022.112494
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    References listed on IDEAS

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    1. Mohammed, W.W. & El-Morshedy, M., 2021. "The influence of multiplicative noise on the stochastic exact solutions of the Nizhnik–Novikov–Veselov system," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 192-202.
    2. Abbagari, Souleymanou & Houwe, Alphonse & Akinyemi, Lanre & Saliou, Youssoufa & Bouetou, Thomas Bouetou, 2022. "Modulation instability gain and discrete soliton interaction in gyrotropic molecular chain," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    3. Wael W. Mohammed & Meshari Alesemi & Sahar Albosaily & Naveed Iqbal & M. El-Morshedy, 2021. "The Exact Solutions of Stochastic Fractional-Space Kuramoto-Sivashinsky Equation by Using ( G ′ G )-Expansion Method," Mathematics, MDPI, vol. 9(21), pages 1-10, October.
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    Cited by:

    1. Zayed, Elsayed M.E. & Alngar, Mohamed E.M. & Shohib, Reham M.A., 2023. "Cubic-quartic embedded solitons with χ(2) and χ(3) nonlinear susceptibilities having multiplicative white noise via Itô calculus," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    2. Zhao Li & Chen Peng, 2023. "Dynamics and Embedded Solitons of Stochastic Quadratic and Cubic Nonlinear Susceptibilities with Multiplicative White Noise in the Itô Sense," Mathematics, MDPI, vol. 11(14), pages 1-11, July.

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