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Complex solitons in the conformable (2+1)-dimensional Ablowitz-Kaup-Newell-Segur equation

1 School of Information Science and Technology, Yunnan Normal University, Yunnan, China
2 Final International University, Kyrenia Mersin 10, Turkey
3 Harran University, Faculty of Education, Sanliurfa, Turkey
4 Tuscia University, Engineering School (DEIM), Viterbo, Italy

Special Issues: Recent Advances in Fractional Calculus with Real World Applications

In this paper, we study on the conformable (2+1)-dimensional Ablowitz-KaupNewell-Segur equation in order to show the existence of complex combined dark-bright soliton solutions. To this purpose an effective method which is the sine-Gordon expansion method is used. The 2D and 3D surfaces under some suitable values of parameters are also plotted.
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Keywords conformable (2+1)-dimensional Ablowitz-Kaup-Newell-Segur equation; sine Gordon expansion method; complex soliton solutions

Citation: Wei Gao, Gulnur Yel, Haci Mehmet Baskonus, Carlo Cattani. Complex solitons in the conformable (2+1)-dimensional Ablowitz-Kaup-Newell-Segur equation. AIMS Mathematics, 2020, 5(1): 507-521. doi: 10.3934/math.2020034

References

  • 1. J. H. He, Application of Homotopy Perturbation Method to Nonlinear Wave Equations, Chaos Soliton. Fract., 26 (2005), 695-700.    
  • 2. J. H. He, Homotopy perturbation method for bifurcation of nonlinear problems, Int. J. Nonlinear Sci., 6 (2005), 207-208.
  • 3. S. J. Liao, Beyond Perturbation: Introduction to the Homotopy Analysis Method, Chapman and Hall/CRC Press, 2003.
  • 4. Z. F. Kocak, H. Bulut, G. Yel, The solution of fractional wave equation by using modified trial equation method and homotopy analysis method, AIP Conference Proceedings, 1637 (2014), 504-512.    
  • 5. J. H. He, Exp-function Method for Fractional Differential Equations, Int. J. Nonlinear Sci., 14 (2013), 363-366.
  • 6. S. Zhang, H. Q. Zhang, An Exp-function method for new N-soliton solutions with arbitrary functions of a (2+1)-dimensional vcBK system, Comput. Math. Appl., 61 (2011), 1923-1930.    
  • 7. A. Ali, M. A. Iqbal, Q. M. UL Hassan, et al. An efficient technique for higher order fractional differential equation, Springer Plus, 5 (2016), 281.
  • 8. C. Cattani, T. A. Sulaiman, H. M. Baskonus, On the soliton solutions to the Nizhnik-NovikovVeselov and the Drinfeld-Sokolov systems, Opt. Quant. Electron., 50 (2018), 138.
  • 9. H. Bulut, T. A. Sulaiman, H. M. Baskonus,et al. Optical solitons and other solutions to the conformable space-time fractional Fokas-Lenells equation, Optik, 172 (2018), 20-27.    
  • 10. W. Xian-Lin and T. Jia-Shi, Travelling Wave Solutions for Konopelchenko-Dubrovsky Equation Using an Extended sinh-Gordon Equation Expansion Method, Commun. Theor. Phys., 50 (2008), 1047.
  • 11. T. A. Sulaiman, G. Yel, H. Bulut, M-fractional solitons and periodic wave solutions to the Hirota Maccari system, Mod. Phys. Lett. B, 33 (2019), 1950052.
  • 12. R. Hirota, Exact solution of the Korteweg-de Vries equation for multiple collisions of solitons, Phys. Rev. Lett., 27 (1971), 1192-1194.    
  • 13. M. R. Miura, Bäcklund Transformation, Springer-Verlag, Berlin, 1978.
  • 14. M. J. Ablowitz, D. J. Kaup, A. C. Newell, et al. The inverse scattering transform-fourier analysis for nonlinear problems, Stud. Appl. Math., 53 (1974), 249-315.    
  • 15. M. A. Helal, A. R.Seadawy, M. H. Zekry, Stability analysis solutions for the fourth-order nonlinear Ablowitz-Kaup-Newell-Segurwater wave equation, Appl. Math. Sci., 7 (2013), 3355-3365.
  • 16. V. B. Matveev, A. O. Smirnov, Solutions of the Ablowitz-Kaup- Newell-Segur hierarchy equations of the "rogue wave" type: an unified approach, Theor. Math. Phys., 186 (2016), 3355-3365.
  • 17. A. M. Wazwaz, The (2+1) and (3+1)-dimensional CBS equations: multiple soliton solutions and multiple singular soliton solutions, Z. Naturforsch Pt A., 65 (2010), 173-181.
  • 18. T. Özer, New traveling wave solutions to AKNS and SKdV equations, Chaos Soliton. Fract., 42 (2009), 577-583.    
  • 19. Z. Cheng, X. Hao, The periodic wave solutions for a (2+1)-dimensional AKNS equation, Appl. Math. Comput., 234 (2014), 118-126.
  • 20. A. Ali, A. R. Seadawy, D. Lu, Computational methods and traveling wave solutions for the fourthorder nonlinear Ablowitz-Kaup-Newell-Segur water wave dynamical equation via two methods and its applications, Open Phys., 16 (2018), 219-226.    
  • 21. S. Zhang, Z. Wang, Bilinearization and new soliton solutions of Whitham-Broer-Kaup equations with time-dependent coefficients, J. Nonlinear Sci. Appl., 10 (2017), 2324-2339.    
  • 22. D. Y. Chen, X. Y. Zhu, J. B. Zhang, et al. New soliton solutions to isospectral AKNS equations, Chinese Journal of Contemporary Mathematics, 33 (2012), 167-167.
  • 23. H. C. Yaslan, A. Girgin, New exact solutions for the conformable space-time fractional KdV, CDG, (2+1)-dimensional CBS and (2+1)-dimensional AKNS equations, Journal of Taibah University for Science, 13 (2018), 1-8.    
  • 24. F. Ferdous, M. G. Hafez, Oblique closed form solutions of some important fractional evolution equations via the modified Kudryashov method arising in physical problems, Journal of Ocean Engineering and Science, 3 (2018), 244-252.    
  • 25. R. Khalil, M. Al Horani, A. Yousef, et al. A new definition of fractional derivative, J. Comput. Appl. Math., 264 (2014), 65-70.    
  • 26. A. Atangana, D. Baleanu, A. Alsaedi, New properties of conformable derivative, Open Math., 13 (2015), 889-898.
  • 27. C. Cattani, T. A. Sulaiman, H. M. Baskonus, et al. Solitons in an inhomogeneous Murnaghan's rod, European Physical Journal Plus, 133 (2018), 1-12.    
  • 28. H. M. Baskonus, New acoustic wave behaviors to the Davey-Stewartson equation with power-law nonlinearity arising in fluid dynamics, Nonlinear Dynam., 86 (2016), 177-183.    
  • 29. C. Yan, A simple transformation for nonlinear waves, Phys. Lett. A, 224 (1996), 77-84.    
  • 30. H. Bulut, T. A. Sulaiman, H. M. Baskonus, New solitary and optical wave structures to the Korteweg-de Vries equation with dual-power law nonlinearity, Opt. Quant. Electron., 48 (2016), 1-14.    
  • 31. Z. Yan, H. Zhang, New explicit and exact travelling wave solutions for a system of variant Boussinesq equations in mathematical physics, Phys. Lett. A, 252 (1999), 291-296.    
  • 32. H. M. Baskonus, T. A. Sulaiman, H. Bulut, New Solitary Wave Solutions to the (2+1)-Dimensional Calogero-Bogoyavlenskii-Schi and the Kadomtsev-Petviashvili Hierarchy Equations, Indian J. Phys., 91 (2017), 1237-1243.    
  • 33. Y. Zhen-Ya, Z. Hong-Oing, F. En-Gui, New explicit and travelling wave solutions for a class of nonlinear evolution equations, Acta. Phys. Sin, 48 (1999), 1-5.
  • 34. C. Cattani, T. A. Sulaiman, H. M. Baskonus, et al. On the soliton solutions to the Nizhnik-NovikovVeselov and the Drinfel'd-Sokolov systems, Opt. Quant. Electron., 50 (2018), 138.
  • 35. Z. Hammouch, T. Mekkaoui, Travelling-wave solutions for some fractional partial differential equation by means of generalized trigonometry functions, International Journal of Applied Mathematical Research, 1 (2012), 206-212.
  • 36. A. Houwe, M. Justin, S. Y. Doka, et. al, New traveling wave solutions of the perturbed nonlinear Schrodinger equation in the left-handed metamaterials, Asian-European Journal of Mathematics, (2018), 2050022.
  • 37. M. A. Khan, O. Kolebaje, A. Yildirim, et al, Fractional investigations of zoonotic visceral leishmaniasis disease with singular and non-singular kernel, The European Physical Journal Plus, 134 (2019), 481.
  • 38. R. Jan, M. A. Khan, P. Kumam, et. al, Modeling the transmission of dengue infection through fractional derivatives, Chaos Soliton. Fract., 127 (2019), 189-216.    
  • 39. W. Wang, M. A. Khan, P. Kumam, et al. A comparison study of bank data in fractional calculus, Chaos Soliton. Fract., 126 (2019), 369-384.    
  • 40. A. Atangana, M. A. Khan, Validity of fractal derivative to capturing chaotic attractors, Chaos Soliton. Fract., 126 (2019), 50-59.    
  • 41. M. A. Khan, F. Gómez-Aguilar, Tuberculosis model with relapse via fractional conformable derivative with power law, Math. Method. Appl. Sci., 42 (2019), 7113-7125.    
  • 42. M. A. Khan, A. Khan, A. Elsonbaty, et al, Modeling and simulation results of a fractional dengue model, The European Physical Journal Plus, 134 (2019), 379.
  • 43. A. Yokus, S. Gulbahar, Numerical Solutions with Linearization Techniques of the Fractional Harry Dym Equation, Applied Mathematics and Nonlinear Sciences, 4 (2019), 35-42.    
  • 44. X. J. Yang, New general fractional-order rheological models with kernels of Mittag-Leffler functions, Rom. Rep. Phys, 69 (2017), 118.
  • 45. K. M. Owolabi, Z. Hammouch, Mathematical modeling and analysis of two-variable system with noninteger-order derivative, Chaos: An Interdisciplinary Journal of Nonlinear Science, 29 (2019), 013145.
  • 46. D. W. Brzeziński, Review of numerical methods for NumILPT with computational accuracy assessment for fractional calculus, Applied Mathematics and Nonlinear Sciences, 3 (2018), 487-502.    
  • 47. M. A. Khan, Z. Hammouch, D. Baleanu, Modeling the dynamics of hepatitis E via the Caputo-Fabrizio derivative, Mathematical Modelling of Natural Phenomena, 14 (2019), 311.
  • 48. X. J. Yang, New rheological problems involving general fractional derivatives with nonsingular power-law kernels, Proceedings of the Romanian Academy Series A-Mathematics Physics Technical Sciences Information Science, 19 (2018),45-52.
  • 49. D. W. Brzeziński, Comparison of Fractional Order Derivatives Computational Accuracy - Right Hand vs Left Hand Definition, Applied Mathematics and Nonlinear Sciences, 2 (2017), 237-248.    
  • 50. C. Cattani, Haar wavelet-based technique for sharp jumps classification, Math. Comput. Model., 39 (2004), 255-278.    
  • 51. M. Eslami, H. Rezazadeh, The first integral method for Wu-Zhang system with conformable timefractional derivative, Calcolo, 53 (2016), 475-485.    
  • 52. P. Veeresha, D. G. Prakasha, H. M. Baskonus, Novel Simulations to the time-fractional Fisher's equation, Mathematical Sciences, 13 (2019), 33-42.    
  • 53. I. K. Youssef, M. H. El Dewaik, Solving Poisson's Equations with fractional order using Haarwavelet, Applied Mathematics and Nonlinear Sciences, 2 (2079), 271-284.
  • 54. X. J. Yang, F. Gao, Y. Ju, H. W. Zhou, Fundamental solutions of the general fractional-order diffusion equations, Mathematical Methods in the Applied Sciences, 41 (2018), 9312-9320.    
  • 55. J. Singh, D. Kumar, Z. Hammouch, et al. A fractional epidemiological model for computer viruses pertaining to a new fractional derivative, Applied Mathematics and Computation, 316 (2018), 504-515.    
  • 56. A. Atangana, Fractional discretization: The African's tortoise walk, Chaos Soliton. Fract., 130 (2020), 109399.
  • 57. C. Ravichandran, K. Jothimani, H. M. Baskonus, et al. New results on nondensely characterized integrodifferential equations with fractional order, European Physical Journal Plus, 133 (2018), 1-10.    
  • 58. K. S. Al-Ghafri, H. Rezazadeh, Solitons and other solutions of (3+1)-dimensional space-time fractional modified KdV-Zakharov-Kuznetsov equation, Applied Mathematics and Nonlinear Sciences, 4 (2019), 289-304.    
  • 59. W. Gao, B. Ghanbari, H. M. Baskonus, New numerical simulations for some real world problems with Atangana-Baleanu fractional derivative, Chaos Soliton. Fract., 128 (2019), 34-43.    
  • 60. A. Atangana, D. Baleanu, New fractional derivatives with non-local and non-singular kernel theory and application to heat transfer model, Therm. Sci., 20 (2016), 763-769.    
  • 61. A. Atangana, B. T. Alkahtani, Analysis of the Keller-Segel model with a fractional derivative without singular kernel, Entropy, 17 (2015), 4439-4453.    

 

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