Research Article
Year 2023,
Volume: 3 Issue: 2, 101 - 110, 30.06.2023
Abstract
The basic principle of this study is to obtain various solutions to the (1+1) dimensional Mikhailov-Novikov-Wang integrable equation (MNWIE). For this purpose, the generalized exponential rational function method (GERFM) is applied to this equation. Thus, several trigonometric functions, hyperbolic functions, and dark soliton solutions to the studied equation are acquired. In this way, some new solutions to the equation that have not been presented before have been obtained. In addition, 2D and 3D graphics of the acquired solutions are drawn for specific values. The obtained results and the graphic drawings of the results have been provided by using Wolfram Mathematica 12.
Keywords
Generalized exponential rational function method (1+1)-dimensional Mikhailov-Novikov-Wang integrable equation trigonometric function solution hyperbolic function solution dark soliton solution
References
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- Akbulut, A., Kaplan, M. and Tascan, F. The investigation of exact solutions of nonlinear partial differential equations by using exp(−ϕ(ξ)) method. Optik, 132, 382–387, (2017).
- Ünal, M. and Ekici, M. The double (G′/G, 1/G)-expansion method and its applications for some nonlinear partial differential equations. Journal of the Institute of Science and Technology, 11(1), 599-608, (2021).
- Nuruddeen, R.I., Aboodh, K.S. and Ali, K.K. Analytical investigation of soliton solutions to three quantum Zakharov-Kuznetsov equations. Communications in Theoretical Physics, 70(4), 405-412, (2018).
- Tahir, M. and Awan, A.U. Optical singular and dark solitons with Biswas–Arshed model by modified simple equation method. Optik, 202, 163523, (2020).
- Tasbozan, O., Çenesiz, Y. and Kurt, A. New solutions for conformable fractional Boussinesq and combined KdV-mKdV equations using Jacobi elliptic function expansion method. The European Physical Journal Plus, 131, 244, (2016).
- Yokuş, A., Durur, H. and Duran, S. Simulation and refraction event of complex hyperbolic type solitary wave in plasma and optical fiber for the perturbed Chen-Lee-Liu equation. Optical and Quantum Electronics, 53, 402, (2021).
- Mikhailov, A.V., Novikov, V.S. and Wang, J.P. On classification of integrable nonevolutionary equations. Studies in Applied Mathematics, 118(4), 419–457, (2007).
- Mikhailov, A.V. and Novikov, V.S. Perturbative symmetry approach. Journal of Physics A: Mathematical and General, 35(22), 4775, (2002).
- Ray, S.S. and Singh, S. New various multisoliton kink-type solutions of the (1+1)-dimensional Mikhailov–Novikov–Wang equation. Mathematical Methods in the Applied Sciences, 44(18), 14690-14702, (2021).
- Raza, N., Seadawy, A.R., Arshed S. and Rafiq, M.H. A variety of soliton solutions for the Mikhailov-Novikov-Wang dynamical equation via three analytical methods. Journal of Geometry and Physics, 176, 104515, (2022).
- Akbulut, A., Kaplan, M. and Kaabar, M.K.A. New exact solutions of the Mikhailov-Novikov- Wang equation via three novel techniques. Journal of Ocean Engineering and Science, 8(1), 103-110, (2021).
- Bekir, A., Shehata, M.S.M. and Zahran, E.H.M. Comparison between the new exact and numerical solutions of the Mikhailov–Novikov–Wang equation. Numerical Methods for Partial Differential Equations, (2021).
- Srivastava, H.M., Günerhan, H. and Ghanbari, B. Exact traveling wave solutions for resonance nonlinear Schrödinger equation with intermodal dispersions and the Kerr law nonlinearity. Mathematical Methods in the Applied Sciences, 42(18), 7210-7221, (2019).
- Ghanbari, B., Osman, M.S. and Baleanu, D. Generalized exponential rational function method for extended Zakharov Kuzetsov equation with conformable derivative. Modern Physics Letters A, 34(20), 1950155, (2019).
- Ismael, H.F., Bulut, H. and Baskonus, H.M. W-shaped surfaces to the nematic liquid crystals with three nonlinearity laws. Soft Computing, 25, 4513-4524, (2021).
- Sağlam Özkan, Y. The generalized exponential rational function and Elzaki–Adomian decomposition method for the Heisenberg ferromagnetic spin chain equation. Modern Physics Letters B, 35(12), 2150200, (2021).
- Duran, S. Breaking theory of solitary waves for the Riemann wave equation in fluid dynamics. International Journal of Modern Physics B, 35(09), 2150130, (2021).
- Duran, S. An investigation of the physical dynamics of a traveling wave solution called a bright soliton. Physica Scripta, 96(12), 125251, (2021).
Year 2023,
Volume: 3 Issue: 2, 101 - 110, 30.06.2023
Abstract
References
- Khater, M.M.A. and Alabdali, A.M. Multiple novels and accurate traveling wave and numerical solutions of the (2+ 1) dimensional Fisher-Kolmogorov-Petrovskii-Piskunov equation. Mathematics, 9(12), 1-13, (2021).
- Dusunceli, F., Celik, E., Askin, M. and Bulut, H. New exact solutions for the doubly dispersive equation using the improved Bernoulli sub-equation function method. Indian Journal of Physics, 95(2), 309-314, (2021).
- Bakıcıerler, G., Alfaqeih, S. and Mısırlı, E. Analytic solutions of a (2+1)-dimensional nonlinear Heisenberg ferromagnetic spin chain equation. Physica A: Statistical Mechanics and its Applications, 582, 126255, (2021).
- Malik, S., Kumar, S., Nisar, K.S. and Saleel, C.A. Different analytical approaches for finding novel optical solitons with generalized third-order nonlinear Schrödinger equation. Results in Physics, 29, 104755, (2021).
- Aktürk, T., Gurefe, Y. and Pandir, Y. An application of the new function method to the Zhiber–Shabat equation. An International Journal of Optimization and Control: Theories & Applications, 7(3), 271–274, (2017).
- Akbulut, A., Kaplan, M. and Tascan, F. The investigation of exact solutions of nonlinear partial differential equations by using exp(−ϕ(ξ)) method. Optik, 132, 382–387, (2017).
- Ünal, M. and Ekici, M. The double (G′/G, 1/G)-expansion method and its applications for some nonlinear partial differential equations. Journal of the Institute of Science and Technology, 11(1), 599-608, (2021).
- Nuruddeen, R.I., Aboodh, K.S. and Ali, K.K. Analytical investigation of soliton solutions to three quantum Zakharov-Kuznetsov equations. Communications in Theoretical Physics, 70(4), 405-412, (2018).
- Tahir, M. and Awan, A.U. Optical singular and dark solitons with Biswas–Arshed model by modified simple equation method. Optik, 202, 163523, (2020).
- Tasbozan, O., Çenesiz, Y. and Kurt, A. New solutions for conformable fractional Boussinesq and combined KdV-mKdV equations using Jacobi elliptic function expansion method. The European Physical Journal Plus, 131, 244, (2016).
- Yokuş, A., Durur, H. and Duran, S. Simulation and refraction event of complex hyperbolic type solitary wave in plasma and optical fiber for the perturbed Chen-Lee-Liu equation. Optical and Quantum Electronics, 53, 402, (2021).
- Mikhailov, A.V., Novikov, V.S. and Wang, J.P. On classification of integrable nonevolutionary equations. Studies in Applied Mathematics, 118(4), 419–457, (2007).
- Mikhailov, A.V. and Novikov, V.S. Perturbative symmetry approach. Journal of Physics A: Mathematical and General, 35(22), 4775, (2002).
- Ray, S.S. and Singh, S. New various multisoliton kink-type solutions of the (1+1)-dimensional Mikhailov–Novikov–Wang equation. Mathematical Methods in the Applied Sciences, 44(18), 14690-14702, (2021).
- Raza, N., Seadawy, A.R., Arshed S. and Rafiq, M.H. A variety of soliton solutions for the Mikhailov-Novikov-Wang dynamical equation via three analytical methods. Journal of Geometry and Physics, 176, 104515, (2022).
- Akbulut, A., Kaplan, M. and Kaabar, M.K.A. New exact solutions of the Mikhailov-Novikov- Wang equation via three novel techniques. Journal of Ocean Engineering and Science, 8(1), 103-110, (2021).
- Bekir, A., Shehata, M.S.M. and Zahran, E.H.M. Comparison between the new exact and numerical solutions of the Mikhailov–Novikov–Wang equation. Numerical Methods for Partial Differential Equations, (2021).
- Srivastava, H.M., Günerhan, H. and Ghanbari, B. Exact traveling wave solutions for resonance nonlinear Schrödinger equation with intermodal dispersions and the Kerr law nonlinearity. Mathematical Methods in the Applied Sciences, 42(18), 7210-7221, (2019).
- Ghanbari, B., Osman, M.S. and Baleanu, D. Generalized exponential rational function method for extended Zakharov Kuzetsov equation with conformable derivative. Modern Physics Letters A, 34(20), 1950155, (2019).
- Ismael, H.F., Bulut, H. and Baskonus, H.M. W-shaped surfaces to the nematic liquid crystals with three nonlinearity laws. Soft Computing, 25, 4513-4524, (2021).
- Sağlam Özkan, Y. The generalized exponential rational function and Elzaki–Adomian decomposition method for the Heisenberg ferromagnetic spin chain equation. Modern Physics Letters B, 35(12), 2150200, (2021).
- Duran, S. Breaking theory of solitary waves for the Riemann wave equation in fluid dynamics. International Journal of Modern Physics B, 35(09), 2150130, (2021).
- Duran, S. An investigation of the physical dynamics of a traveling wave solution called a bright soliton. Physica Scripta, 96(12), 125251, (2021).
There are 23 citations in total.
Details
| Primary Language | English |
|---|---|
| Subjects | Numerical Solution of Differential and Integral Equations, Numerical Analysis, Numerical and Computational Mathematics (Other) |
| Journal Section | Research Articles |
| Authors | |
| Early Pub Date | June 30, 2023 |
| Publication Date | June 30, 2023 |
| Submission Date | June 23, 2022 |
| Published in Issue | Year 2023 Volume: 3 Issue: 2 |
Cited By
Dynamic nature of analytical soliton solutions of the (1+1)-dimensional Mikhailov-Novikov-Wang equation using the unified approach
International Journal of Mathematics and Computer in Engineering
https://doi.org/10.2478/ijmce-2023-0018
Math Model Numer Simul Appl - 2024
The published articles in MMNSA are licensed under a Creative Commons Attribution 4.0 International License
The published articles in MMNSA are licensed under a Creative Commons Attribution 4.0 International License