THERMAL SCIENCE

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Pinar Albayrak

SOLITON SOLUTIONS OF (2+1)-DIMENSIONAL NON-LINEAR REACTION-DIFFUSION MODEL VIA RICCATI-BERNOULLI APPROACH

ABSTRACT
In this study, soliton solutions of the (2+1)-dimensional reaction-diffusion equation are investigated by the extended Kudryashov method based on Riccati-Bernoulli approach. Firstly, we obtained the non-linear ordinary differential form of the (2+1)-dimensional non-linear reaction-diffusion equation by implementing the wave transformation. Then, the extended Kudryashov method has been presented and applied to the non-linear ordinary differential form. By applying the extended Kudryashov method the polynomial form has been gained, solution sets have been obtained and soliton solutions have been formed by taking the appropriate sets. Finally, some graphical representations of the gained results for instance bright, dark, kink and singular solutions are presented and commented. Within the scope of the article, the study on investigating the soliton solutions of the (2+1)-dimensional non-linear reaction-diffusion equation via the extended Kudryashov approach has not been studied and the obtained results have not been reported.
KEYWORDS
wave transform, the extended Kudryashov method, kink soliton, traveling wave solution
PAPER SUBMITTED: 2022-06-10
PAPER REVISED: 2022-09-22
PAPER ACCEPTED: 2022-10-17
PUBLISHED ONLINE: 2023-01-29
DOI REFERENCE: https://doi.org/10.2298/TSCI22S2811A
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2022, VOLUME 26, ISSUE Special issue 2, PAGES [811 - 821]
REFERENCES
  1. Ozisik, M., et al., Optical Solitons with Kudryashov's Sextic Power-Law Non-Linearity, Optik, 261 (2022), ID 169202
  2. Esen, H., et al., Analytical Soliton Solutions of the Higher Order Cubic-Quintic Non-Linear Schrodinger Equation and the Influence of the Model's Parameters, Journal of Applied Physics, 132 (2022), 5, ID 053103
  3. Ozdemir, N., et al., Two Analytical Schemes for the Optical Soliton Solution of the (2+1)-Hirota-Maccari System Observed in Single-Mode Fibers, Universe, 8 (2022), 11, ID 584
  4. Ozisik, M., et al., On the Examination of Optical Soliton Pulses of Manakov System with Auxiliary Equation Technique, Optik, 268 (2022), ID 169800
  5. Secer, A., Stochastic Optical Solitons with Multiplicative White Noise via Itô Calculus, Optik 268 (2022), ID 169831
  6. Bayram, M., Optical Bullets with Biswas-Milovic Equation Having Kerr and Parabolic Laws of Non-Linearity, Optik 270 (2022), ID 170046
  7. Ozisik, M., On the Optical Soliton Solution of the (1+1)-Dimensional Perturbed NLSE in Optical Nano-fibers, Optik, 250 (2022), Part 1, ID 168233
  8. Zhang, S., Application of Exp-Function Method to High-Dimensional Non-Linear Evolution Equations, Chaos Solitons Fractals, 38 (2008), 1, pp. 270-276
  9. Kudryashov, N. A., One Method for Finding Exact Solutions of Non-Linear Differential Equations, Comm. in Non-Linear Science and Numerical Simulation, 17 (2011), 6, pp. 2248-2253
  10. Biswas, A., et al., Dispersive Optical Solitons with Schrodinger-Hirota Model by Trial Equation Meth-d, Optik, 162 (2018), June, pp. 35-41
  11. Zayed, E. M. E., et al., Pure-Cubic Optical Soliton Perturbation with Full Non-Linearity by Unified Riccati Equation Expansion, Optik, 223 (2020), ID 165445
  12. Kumar, H., Chand, F., Applications of Extended F-Expansion and Projective Ricatti Equation Methods to (2+1)-Dimensional Soliton Equations, AIP Advances, 3 (2013), 3, ID 032128
  13. Mirzazadeh, M., et al., Topological Solitons of Resonant Non-Linear Schodinger's Equation with Dual-Power Law Non-Linearity by G′/G-Expansion Technique, Optik, 125 (2014), 19, pp. 5480-5489
  14. Ozisik, M., et al., An Encyclopedia of Kudryashov's Integrability Approaches Applicable to Optoelectronic Devices, Optik, 265 (2022), ID 169499
  15. Huang, Y., Yu, X., Solitons and Peakons of a Nonautonomous Camassa-Holm Equation, Applied Mathematics Letters, 98 (2019), Dec., pp. 385-391
  16. Onder, I., et al., On the Optical Soliton Solutions of Kundu-Mukherjee-Naskar Equation via Two Different Analytical Methods, Optik, 257 (2022), ID 168761
  17. Ozisik, M., Novel (2+1) and (3+1) Forms of the Biswas-Milovic Equation and Optical Soliton Solutions via Two Efficient Techniques, Optik, 269 (2022), ID 169798
  18. Yang, S., Chirped Envelope Solutions of the Triki-Biswas Equation, Optik, 244 (2021), ID 167542
  19. Ozisik, M., et al., On the Analytical Optical Soliton Solutions of Perturbed Radhakrishnan-Kundu-Lakshmanan Model with Kerr Law Non-Linearity, Optical and Quant. Electronics, 54 (2022), ID 371
  20. Kudryashov, N. A., On "New Travelling Wave Solutions" of the KdV and the KdV-Burgers Equations, Comm. in Non-Linear Science and Numerical Simulation, 14 (2009), 5, pp. 1891-1900
  21. Tebue, E. T., et al., Solitons and other Solutions of the Non-Linear Fractional Zoomeron Equation, Chinese Journal of Physics, 56 (2018), 3, pp. 1232-1246
  22. Zhou, J., Tian, L., Solitons, Peakons and Periodic Cusp Wave Solutions for the Fornberg-Whitham Equation, Non-linear Analysis: Real World Applications, 11 (2010), 1, pp. 356-363
  23. Akbulut, A., et al., New Exact Solutions of the Mikhailov-Novikov-Wang Equation via Three Novel Techniques, Journal of Ocean Engineering and Science, On-line first, doi.org/10.1016/j.joes. 2021, 2021
  24. Tantawy, S.A., et al., Novel Analytical Cnoidal and Solitary Wave Solutions of the Extended Kawahara Equation, Chaos, Solitons & Fractals, 147 (2021), ID 110965
  25. Ozisik, M., et al., Dispersive Optical Solitons of Biswas-Arshed Equation with a Couple of Novel Approaches, Optik, 265 (2022), ID 169547
  26. Yun-Quan, K., Jun, Y., The First Integral Method to Study a Class of Reaction-Diffusion Equations, Commun. Theor. Phys., 43 (2005), 4, pp. 597-600
  27. Tukur, A.S., et al., Dynamics of Lump Solutions to the Variable Coefficients (2+1)-Dimensional Burger's and Chaffee-Infante Equations, Journal of Geometry and Physics, 168 (2021), ID 104315
  28. Triki, H., Wazwaz, A. M., On Soliton Solutions for the Fitzhugh-Nagumo Equation with Time-Dependent Coefficients, Applied Mathematical Modelling, 37 (2013), 6, pp. 3821-3828
  29. Guner, O., New Exact Solution for (2+1) and (3+1) Dimensional Non-Linear Partial Differential Equations, Aksaray J. Sci. Eng., 2 (2018), 2, pp. 161-170
  30. Biswas, A., 1-Soliton Solution of the Non-Linear Reaction-Diffusion Equation, International Journal of Chemical Reactor Engineering, 6 (2008), 1
  31. Triki, H., et al., Soliton Solutions of Non-Linear Diffusion-Reaction-Type Equations with Time-Dependent Coefficients Accounting for Long-Range Diffusion, Non-linear Dynamics, 86 (2016), 3, pp. 2115-2126
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Soliton solutions of (2+1)-dimensional non-linear reaction-diffusion model via Riccati-Bernoulli approach

© 2024 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence