New Solutions for IOPM and (3+1)-Dimensional NLWE in Liquid with Gas Bubbles

Öz

Generalized Kudryashov method (GKM), which is one of the solution methods of nonlinear evolution equations (NLEEs), has been used to obtain some solutions of Ivancevic option pricing model (IOPM) and (3+1)-dimensional nonlinear wave equation (NLWE) in liquid with gas bubbles. Thus, some solutions of the discussed equations have been found such as dark soliton, trigonometric and hyperbolic solutions. Two dimensional (2D) and three dimensional (3D) graphics of these solutions have been drawn with the help of Wolfram Mathematica 12.

Anahtar Kelimeler

• GKM
• Ivancevic option pricing model
• (3+1)-dimensional NLWE in liquid with gas bubbles
• soliton solutions

Kaynakça

1. Biswas A, Yıldırım Y, Yaşar E, Alqahtani R T, 2018. Optical solitons for Lakshmanan–Porsezian–Daniel model with dual-dispersion by trial equation method, Optik, (168), 432-439.
2. Chen Q, Baskonus H M, Gao W, Ilhan E, 2022. Soliton theory and modulation instability analysis: The Ivancevic option pricing model in economy. Alexandria Engineering Journal, 61(10):7843-7851.
3. Chen Y Q, Tang Y H, Manafian J, Rezazadeh H, Osman M S, 2021. Dark wave, rogue wave and perturbation solutions of Ivancevic option pricing model. Nonlinear Dynamics, 105(3): 2539-2548.
4. Duarte L G S, da Mota L A C P. 2021. An efficient method for computing Liouvillian first integrals of planar polynomial vector fields, Journal of Differential Equations, (300), 356-385.
5. Eslami M, Mirzazadeh M, 2014. Exact solutions of modified Zakharov–Kuznetsov equation by the homogeneous balance method, Ain Shams Engineering Journal, (5), 221-225.
6. González-Gaxiola O, Edeki S O, Ugbebor O O, de Chávez J R, 2017. Solving the Ivancevic Pricing Model Using the He's Frequency Amplitude Formulation. European Journal of Pure & Applied Mathematics, 10(4).
7. Gurefe Y, 2020. The generalized Kudryashov method for the nonlinear fractional partial differential equations with the beta-derivative. Revista Mexicana de Fisica, 66, 6, 771-781.
8. Günay B, Kuo C K, Ma W X, 2021. An application of the exponential rational function method to exact solutions to the Drinfeld–Sokolov system, Results in Physics, 104733, (29).

9. Ivancevic V G, 2010. Adaptive-wave alternative for the black-scholes option pricing model. Cognitive Computation, 2(1): 17-30.
10. Ivancevic V G, 2011. Adaptive wave models for sophisticated option pricing. Journal of Mathematical Finance, 1(03): 41.
11. Jena R M, Chakraverty S, Baleanu D, 2020. A novel analytical technique for the solution of time-fractional Ivancevic option pricing model. Physica A: Statistical Mechanics and its Applications, 550, 124380.
12. Kara S, Ünsal Ö, 2022. Analytical solutions to new forms of two nonlinear partial differential equations via two variable expansion method, Partial Differential Equations in Applied Mathematics, 100210(5).
13. Kumar S, Hamid I, Abdou M A, 2021. Specific wave profiles and closed-form soliton solutions for generalized nonlinear wave equation in (3+ 1)-dimensions with gas bubbles in hydrodynamics and fluids. Journal of Ocean Engineering and Science, in press.
14. Liu W, Zhang Y, 2020. Resonant multiple wave solutions, complexiton solutions and rogue waves of a generalized (3+ 1)-dimensional nonlinear wave in liquid with gas bubbles. Waves in Random and Complex Media, 30(3): 470-480.
15. Liu W, Zhang Y, Zhang H, 2020. High-order rogue waves of the generalized (3+ 1)-dimensional nonlinear wave in liquid with gas bubbles. The European Physical Journal Plus, 135(2): 1-11.
16. Mamun A A, Ananna S N, An T, Asaduzzaman M, Miah M M, 2022. Solitary wave structures of a family of 3D fractional WBBM equation via the tanh-coth approach, Partial Differential Equations in Applied Mathematics, 100237(5).
17. Shen G, Manafian J, Huy D T N, Nisar K S, Abotaleb M, Trung N D, 2022. Abundant soliton wave solutions and the linear superposition principle for generalized (3+ 1)-D nonlinear wave equation in liquid with gas bubbles by bilinear analysis. Results in Physics, 32, 105066.
18. Tu J M, Tian S F, Xu M J, Song X Q, Zhang T T, 2016. Bäcklund transformation, infinite conservation laws and periodic wave solutions of a generalized (3+ 1)-dimensional nonlinear wave in liquid with gas bubbles. Nonlinear Dynamics, 83(3): 1199-1215.
19. Tuluce Demiray S, Bayrakci U, 2021a. Construction of Soliton Solutions for Chaffee-Infante Equation, AKU J. Sci. Eng., 21(5): 1046-1051.
20. Tuluce Demiray S, Bayrakci U, 2021b. Soliton Solutions for space-time fractional Heisenberg ferromagnetic spin chain equation by generalized Kudryashov method and modified exp (-Ω(η))-expansion function method, Revista Mexicana de Fisica, 67(3): 393-402.
21. Tuluce Demiray S, Bayrakci U, 2021c. Soliton Solutions of Generalized Third-Order Nonlinear Schrödinger Equation by Using GKM, Journal of the Institute of Science and Technology, 11(2): 1481-1488.
22. Yadav S, Arora R, 2021. Lie symmetry analysis, optimal system and invariant solutions of (3+ 1)-dimensional nonlinear wave equation in liquid with gas bubbles. The European Physical Journal Plus, 136(2): 1-25.
23. Wang H, Tian S, Zhang T, Chen Y, 2019. Lump wave and hybrid solutions of a generalized (3+ 1)-dimensional nonlinear wave equation in liquid with gas bubbles. Frontiers of Mathematics in China, 14(3): 631-643.
24. Wang M, Tian B, Sun Y, Zhang Z, 2020. Lump, mixed lump-stripe and rogue wave-stripe solutions of a (3+ 1)-dimensional nonlinear wave equation for a liquid with gas bubbles. Computers & Mathematics with Applications, 79(3): 576-587.