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基于(G'/G)展开法求解(1 + 1)维积分微分Ito方程的新精确解
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Abstract:
(G'/G)展开法可以有效的求解出非线性偏微分方程的精确解。本文利用(G'/G)展开法及齐次平衡原则，对(1 + 1)维积分微分Ito方程进行求解，得到该方程新的精确解，这些解包括双曲函数解、三角函数解以及有理函数解。根据待定参数之间的关系对参数进行取值，运用数学软件Maple画出精确解的图像。
The (G'/G) expansion method can effectively solve the exact solution of nonlinear partial differential equations. In this paper, we use the (G'/G) expansion method and the homogeneous balance rule to solve the (1 + 1) -dimensional integro-differential Ito equation, and obtain its new exact solutions, which include hyperbolic, trigonometric and rational solutions. According to the relationship between the undetermined parameters, the parameters are valued. The image of the exact solution is obtained by Maple software.
| [1] | Nkenfack, C.E., Lekeufack, O.T., Yamapi, R. and Kengne, E. (2024) Bright Solitons and Interaction in the Higher-Order Gross-Pitaevskii Equation Investigated with Hirota’s Bilinear Method. Physics Letters A, 511, Article ID: 129563. https://doi.org/10.1016/j.physleta.2024.129563 |
| [2] | Rabie, W.B. and Ahmed, H.M. (2022) Cubic-Quartic Optical Solitons and Other Solutions for Twin-Core Couplers with Polynomial Law of Nonlinearity Using the Extended F-Expansion Method. Optik, 253, 168575. https://doi.org/10.1016/j.ijleo.2022.168575 |
| [3] | Wang, M., Zhou, Y. and Li, Z. (1996) Application of a Homogeneous Balance Method to Exact Solutions of Nonlinear Equations in Mathematical Physics. Physics Letters A, 216, 67-75. https://doi.org/10.1016/0375-9601(96)00283-6 |
| [4] | Mohanty, S.K., Kumar, S., Dev, A.N., Deka, M.K., Churikov, D.V. and Kravchenko, O.V. (2022) An Efficient Technique of ()-Expansion Method for Modified KDV and Burgers Equations with Variable Coefficients. Results in Physics, 37, Article ID: 105504. https://doi.org/10.1016/j.rinp.2022.105504 |
| [5] | Yang, Y., Xia, T. and Liu, T. (2023) Darboux Transformation and Exact Solution to the Nonlocal Kundu-Eckhaus Equation. Applied Mathematics Letters, 141, Article ID: 108602. https://doi.org/10.1016/j.aml.2023.108602 |
| [6] | Khalil, T.A., Badra, N., Ahmed, H.M. and Rabie, W.B. (2022) Bright Solitons for Twin-Core Couplers and Multiple-Core Couplers Having Polynomial Law of Nonlinearity Using Jacobi Elliptic Function Expansion Method. Alexandria Engineering Journal, 61, 11925-11934. https://doi.org/10.1016/j.aej.2022.05.042 |
| [7] | Zahran, E.H.M., Ahmad, H., Saeed, T. and Botmart, T. (2022) New Diverse Variety for the Exact Solutions to Keller-Segel-Fisher System. Results in Physics, 35, Article ID: 105320. https://doi.org/10.1016/j.rinp.2022.105320 |
| [8] | Aniqa, A. and Ahmad, J. (2022) Soliton Solution of Fractional Sharma-Tasso-Olever Equation via an Efficient ()-Expansion Method. Ain Shams Engineering Journal, 13, Article ID: 101528. https://doi.org/10.1016/j.asej.2021.06.014 |
| [9] | Wang, M., Li, X. and Zhang, J. (2008) The ()-Expansion Method and Travelling Wave Solutions of Nonlinear Evolution Equations in Mathematical Physics. Physics Letters A, 372, 417-423. https://doi.org/10.1016/j.physleta.2007.07.051 |
| [10] | Batool, T., Rizvi, S.T.R. and Seadawy, A.R. (2022) Multiple Breathers and Rational Solutions to Ito Integro-Differential Equation Arising in Shallow Water Waves. Journal of Geometry and Physics, 178, Article ID: 104540. https://doi.org/10.1016/j.geomphys.2022.104540 |
| [11] | Gepreel, K.A., Nofal, T.A. and Alasmari, A.A. (2017) Exact Solutions for Nonlinear Integro-Partial Differential Equations Using the Generalized Kudryashov Method. Journal of the Egyptian Mathematical Society, 25, 438-444. https://doi.org/10.1016/j.joems.2017.09.001 |
