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Traveling wave solutions of some important Wick-type fractional stochastic nonlinear partial differential equations

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  • Kim, Hyunsoo
  • Sakthivel, Rathinasamy
  • Debbouche, Amar
  • Torres, Delfim F.M.

Abstract

In this article, exact traveling wave solutions of a Wick-type stochastic nonlinear Schrödinger equation and of a Wick-type stochastic fractional Regularized Long Wave-Burgers (RLW-Burgers) equation have been obtained by using an improved computational method. Specifically, the Hermite transform is employed for transforming Wick-type stochastic nonlinear partial differential equations into deterministic nonlinear partial differential equations with integral and fraction order. Furthermore, the required set of stochastic solutions in the white noise space is obtained by using the inverse Hermite transform. Based on the derived solutions, the dynamics of the considered equations are performed with some particular values of the physical parameters. The results reveal that the proposed improved computational technique can be applied to solve various kinds of Wick-type stochastic fractional partial differential equations.

Suggested Citation

  • Kim, Hyunsoo & Sakthivel, Rathinasamy & Debbouche, Amar & Torres, Delfim F.M., 2020. "Traveling wave solutions of some important Wick-type fractional stochastic nonlinear partial differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    • Handle: RePEc:eee:chsofr:v:131:y:2020:i:c:s096007791930493x
    DOI: 10.1016/j.chaos.2019.109542
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    References listed on IDEAS

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    1. Burgos, C. & Cortés, J.-C. & Debbouche, A. & Villafuerte, L. & Villanueva, R.-J., 2019. "Random fractional generalized Airy differential equations: A probabilistic analysis using mean square calculus," Applied Mathematics and Computation, Elsevier, vol. 352(C), pages 15-29.
    2. Atangana, Abdon & Koca, Ilknur, 2016. "Chaos in a simple nonlinear system with Atangana–Baleanu derivatives with fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 89(C), pages 447-454.
    3. Chen, Yong & Wang, Qi & Li, Biao, 2005. "The stochastic soliton-like solutions of stochastic KdV equations," Chaos, Solitons & Fractals, Elsevier, vol. 23(4), pages 1465-1473.
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    Cited by:

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    2. Akinlar, M.A. & Inc, Mustafa & Gómez-Aguilar, J.F. & Boutarfa, B., 2020. "Solutions of a disease model with fractional white noise," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    3. Ahmed, Hamdy M., 2022. "Construction controllability for conformable fractional stochastic evolution system with noninstantaneous impulse and nonlocal condition," Statistics & Probability Letters, Elsevier, vol. 190(C).
    4. Han, Tianyong & Li, Zhao & Shi, Kaibo & Wu, Guo-Cheng, 2022. "Bifurcation and traveling wave solutions of stochastic Manakov model with multiplicative white noise in birefringent fibers," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    5. Zakaria Ali & Minyahil Abera Abebe & Talat Nazir, 2024. "Strong Convergence of Euler-Type Methods for Nonlinear Fractional Stochastic Differential Equations without Singular Kernel," Mathematics, MDPI, vol. 12(18), pages 1-36, September.

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