IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v180y2024ics0960077924000420.html
   My bibliography  Save this article

Investigating exact solutions, sensitivity, and chaotic behavior of multi-fractional order stochastic Davey–Sewartson equations for hydrodynamics research applications

Author

Listed:
  • Qi, Jianming
  • Cui, Qinghua
  • Bai, Leiqiang
  • Sun, Yiqun

Abstract

Our research aims to explore the fractional derivative of the Stochastic Davey–Stewartson equation (FDSDSEs) and make contributions in seven aspects: Firstly, we discovered previously unknown exact solutions for FDSDSEs, including Weierstrass elliptic function solutions. These findings provide new insights for our understanding and analysis of these equations. Secondly, we analyzed the effect of noise on stochastic solutions. We found that higher noise intensity can disrupt patterns and result in flatter surfaces. However, we observed that multiplicative noise can stabilize the solution to some extent. This reveal the role of noise in stochastic dynamics and has important implications for wave behavior in the ocean environment. Thirdly, we emphasized the impact of fractional derivatives on noise dynamics. Our research indicates the importance of considering the order of derivatives α in analysis and modeling. Different order derivatives have different effects on noise, which is significant for ocean researchers in selecting appropriate derivatives to study stochastic systems. Fourthly, we compared the effects of different fractional derivatives on noise in stochastic solutions. We found that choosing appropriate derivative orders can more accurately describe wave behavior in the ocean environment. This discovery has important implications for improving wave models and predicting ocean waves. Fifthly, we studied the influence of tilted wave variations in FDSDSE solutions. We observed spiral-like patterns, providing new insights into wave propagation in the ocean. This is significant for understanding wave behavior in the ocean and relevant ocean engineering applications. Sixthly, we explored the phase diagrams and chaotic behavior of FDSDSE through sensitivity analysis and perturbation factors. This enhances our understanding of practical applications and control strategies in ocean hydrodynamics research and is also important for delving into the dynamic behavior and phase diagrams of these equations. Finally, we compared our research results with well-known wave phenomena in the ocean through visualization, highlighting the practical relevance of our study. These comparisons involve random propagation of ocean solitary waves, twisting propagation of ocean waves, and rotating propagation of solitary waves, providing some inspiration for advancing the fields of ocean science and engineering.

Suggested Citation

  • Qi, Jianming & Cui, Qinghua & Bai, Leiqiang & Sun, Yiqun, 2024. "Investigating exact solutions, sensitivity, and chaotic behavior of multi-fractional order stochastic Davey–Sewartson equations for hydrodynamics research applications," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
  • Handle: RePEc:eee:chsofr:v:180:y:2024:i:c:s0960077924000420
    DOI: 10.1016/j.chaos.2024.114491
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077924000420
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.chaos.2024.114491?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Zheng, Bailin & Kai, Yue & Xu, Wenlong & Yang, Nan & Zhang, Kai & Thibado, P.M., 2019. "Exact traveling and non-traveling wave solutions of the time fractional reaction–diffusion equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 532(C).
    2. Seadawy, Aly R. & Iqbal, Mujahid & Lu, Dianchen, 2020. "Propagation of kink and anti-kink wave solitons for the nonlinear damped modified Korteweg–de Vries equation arising in ion-acoustic wave in an unmagnetized collisional dusty plasma," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 544(C).
    3. Zhao Li & Peng Li & Tianyong Han, 2021. "White Noise Functional Solutions for Wick-Type Stochastic Fractional Mixed KdV-mKdV Equation Using Extended - Expansion Method," Advances in Mathematical Physics, Hindawi, vol. 2021, pages 1-6, December.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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).
    2. Seadawy, Aly R. & Ali, Safdar & Rizvi, Syed T.R., 2022. "On modulation instability analysis and rogue waves in the presence of external potential: The (n + 1)-dimensional nonlinear Schrödinger equation," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    3. Marwan Alquran & Imad Jaradat, 2023. "Identifying Combination of Dark–Bright Binary–Soliton and Binary–Periodic Waves for a New Two-Mode Model Derived from the (2 + 1)-Dimensional Nizhnik–Novikov–Veselov Equation," Mathematics, MDPI, vol. 11(4), pages 1-9, February.
    4. Zhang, Xin & Shi, Ran, 2022. "Novel fast fixed-time sliding mode trajectory tracking control for manipulator," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    5. Iqbal, Muhammad S. & Seadawy, Aly R. & Baber, Muhammad Z. & Qasim, Muhammad, 2022. "Application of modified exponential rational function method to Jaulent–Miodek system leading to exact classical solutions," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    6. Abd-Allah Hyder & Ahmed H. Soliman & Clemente Cesarano & M. A. Barakat, 2021. "Solving Schrödinger–Hirota Equation in a Stochastic Environment and Utilizing Generalized Derivatives of the Conformable Type," Mathematics, MDPI, vol. 9(21), pages 1-16, October.
    7. He, Xue-Jiao & Lü, Xing, 2022. "M-lump solution, soliton solution and rational solution to a (3+1)-dimensional nonlinear model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 197(C), pages 327-340.
    8. Rizvi, Syed T.R. & Seadawy, Aly R. & Ahmed, Sarfaraz & Younis, Muhammad & Ali, Kashif, 2021. "Study of multiple lump and rogue waves to the generalized unstable space time fractional nonlinear Schrödinger equation," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    9. Seadawy, Aly R. & Ahmed, Sarfaraz & Rizvi, Syed T.R. & Ali, Kashif, 2022. "Lumps, breathers, interactions and rogue wave solutions for a stochastic gene evolution in double chain deoxyribonucleic acid system," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    10. Fang, Yin & Wu, Gang-Zhou & Kudryashov, Nikolay A. & Wang, Yue-Yue & Dai, Chao-Qing, 2022. "Data-driven soliton solutions and model parameters of nonlinear wave models via the conservation-law constrained neural network method," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    11. Lewa’ Alzaleq & Valipuram Manoranjan, 2023. "Analysis of a Reaction–Diffusion–Advection Model with Various Allee Effects," Mathematics, MDPI, vol. 11(10), pages 1-21, May.
    12. Owolabi, Kolade M. & Jain, Sonal, 2023. "Spatial patterns through diffusion-driven instability in modified predator–prey models with chaotic behaviors," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:180:y:2024:i:c:s0960077924000420. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.