Construction of complexiton-type solutions using bilinear form of Hirota-type
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Melike Kaplan
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Nauman Raza
Abstract
In this paper, based on the Hirota bilinear form and the extended transformed rational function method, complexiton solutions have been found of the Hirota–Satsuma–Ito (HSI) equation and generalized Calogero–Bogoyavlenskii–Schiff equation through a direct symbolic computation with Maple. This method is the improved form of the transformed rational function method. The obtained complexiton solutions, includes trigonometric and hyperbolic trigonometric solutions, have verified utilizing Hirota bilinear forms. Also, a graphical representation of the obtained solutions is given.
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Author contributions: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
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Research funding: None declared.
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Conflict of interest statement: The authors declare no conflicts of interest regarding this article.
References
[1] K. Hosseini, M. Mirzazadeh, M. Aligoli, M. Eslami, and J. G. Liu, “Rational wave solutions to a generalized (2+1)-dimensional Hirota bilinear equation,” Math. Model Nat. Phenom., vol. 15, p. 61, 2020. https://doi.org/10.1051/mmnp/2020018.Suche in Google Scholar
[2] Y. Pandir, Y. Gurefe, and E. Misirli, “Classification of exact solutions to the generalized Kadomtsev-Petviashvili equation,” Phys. Scripta, vol. 87, p. 025003, 2013. https://doi.org/10.1088/0031-8949/87/02/025003.Suche in Google Scholar
[3] D. Kumar and M. Kaplan, “Application of the modified Kudryashov method to the generalized Schrödinger-Boussinesq equations,” Opt. Quant. Electron., vol. 50, p. 329, 2018. https://doi.org/10.1007/s11082-018-1595-9.Suche in Google Scholar
[4] A. Zubair and N. Raza, “Bright and dark solitons in (n+1)-dimensions with spatio-temporal dispersion,” J. Opt., vol. 48, pp. 594–605, 2019. https://doi.org/10.1007/s12596-019-00572-8.Suche in Google Scholar
[5] N. Raza and A. Zubair, “Bright, dark and dark-singular soliton solutions of nonlinear Schrödinger’s equation with spatio-temporal dispersion,” J. Mod. Opt., vol. 65, pp. 1975–1982, 2018. https://doi.org/10.1080/09500340.2018.1480066.Suche in Google Scholar
[6] N. Raza and A. Javid, “Optical dark and dark-singular soliton solutions of (1+2)-dimensional chiral nonlinear Schrodinger’s equation, Waves Rand,” Compl. Med., vol. 29, pp. 496–508, 2019. https://doi.org/10.1080/17455030.2018.1451009.Suche in Google Scholar
[7] N. Raza, S. Sial, and M. Kaplan, “Exact periodic and explicit solutions of higher dimensional equations with fractional temporal evolution,” Optik, vol. 156, pp. 628–634, 2018. https://doi.org/10.1016/j.ijleo.2017.11.107.Suche in Google Scholar
[8] A. Javid, N. Raza, and M. S. Osman, “Multi-solitons of thermophoretic motion equation depicting the wrinkle propagation in substrate-supported graphene sheets,” Commun. Theor. Phys., vol. 71, pp. 362–366, 2019. https://doi.org/10.1088/0253-6102/71/4/362.Suche in Google Scholar
[9] K. Hosseini, M. Samavat, M. Mirzazadeh, W. X. Ma, and Z. Hammouch, “New (3 + 1)-dimensional Hirota bilinear equation: its backlund transformation and rational-type solutions,” Regul. Chaotic Dyn., vol. 25, no. 4, pp. 383–391, 2020. https://doi.org/10.1134/s156035472004005x.Suche in Google Scholar
[10] J. G. Liu, M. Eslami, H. Rezazadeh, and M. Mirzazadeh, “The dynamical behavior of mixed type lump solutions on the (3+1)-dimensional generalized Kadomtsev-Petviashvili-Boussinesq equation,” Int. J. Nonlinear Sci. Numer. Stimul., vol. 21, nos. 7–8, pp. 661–665, 2020. https://doi.org/10.1515/ijnsns-2018-0373.Suche in Google Scholar
[11] W. X. Ma, “Complexiton solutions to the Korteweg-de Vries equation,” Phys. Lett. A, vol. 301, pp. 35–44, 2002. https://doi.org/10.1016/s0375-9601(02)00971-4.Suche in Google Scholar
[12] H. O. Roshid, M. H. Khan, and A. M. Wazwaz, “Lump, multi-lump, cross kinky-lump and manifold periodic-soliton solutions for the (2+1)-D Calogero-Bogoyavlenskii-Schiff equation,” Heliyon, vol. 6, p. e03701, 2020. https://doi.org/10.1016/j.heliyon.2020.e03701.Suche in Google Scholar PubMed PubMed Central
[13] H. Q. Zhang and W. X. Ma, “Resonant multiple wave solutions for a (3+1)-dimensional nonlinear evolution equation by linear superposition principle,” Comput. Math. Appl., vol. 73, pp. 2339–2343, 2017. https://doi.org/10.1016/j.camwa.2017.03.014.Suche in Google Scholar
[14] R. Hirota, “Exact solution of the Korteweg-De Vries equation for multiple collisions of solitons,” Phys. Rev. Lett., vol. 27, pp. 1192–1194, 1971. https://doi.org/10.1103/physrevlett.27.1192.Suche in Google Scholar
[15] H. Zhang and W. X. Ma, “Extended transformed rational function method and applications to complexiton solutions,” Appl. Math. Comput., vol. 230, pp. 509–515, 2014, 2014. https://doi.org/10.1016/j.amc.2013.12.156.Suche in Google Scholar
[16] W. X. Ma and J. H. Lee, “A transformed rational function method and exact solutions to the 3+1 dimensional Jimbo-Miwa equation, Chaos,” Solit. Fractals, vol. 42, no. 3, pp. 1356–1363, 2009. https://doi.org/10.1016/j.chaos.2009.03.043.Suche in Google Scholar
[17] E. Yasar, Y. Yıldırım, and A. R. Adem, “Extended transformed rational function method to nonlinear evolution equations,” Int. J. Nonlinear Sci. Numer. Stimul., vol. 20, no. 6, pp. 691–701, 2019. https://doi.org/10.1515/ijnsns-2018-0286.Suche in Google Scholar
[18] M. Kaplan and M. N. Ozer, “Multiple-soliton solutions and analytical solutions to a nonlinear evolution equation,” Opt. Quant. Electron., vol. 50, p. 2, 2018. https://doi.org/10.1007/s11082-017-1270-6.Suche in Google Scholar
[19] O. Unsal, “Application of extended transformed rational function method to some (3+1) dimensional nonlinear evolution equations,” Karaelmas Fen ve Müh. Derg., vol. 8, no. 2, pp. 433–437, 2018.10.7212/zkufbd.v8i2.1041Suche in Google Scholar
[20] X. Y. Liu and D. S. Wang, “The n-soliton solution and localized wave interaction solutions of the (2+1)-dimensional generalized Hirota-Satsuma-Ito equation,” Comput. Math. Appl., vol. 77, no. 4, pp. 947–966, 2019.10.1016/j.camwa.2018.10.035Suche in Google Scholar
[21] Y. Zhou and W. X. Ma, “Applications of linear superposition principle to resonant solitons and complexitons,” Comput. Math. Appl., vol. 73, no. 8, pp. 1697–1706, 2017. https://doi.org/10.1016/j.camwa.2017.02.015.Suche in Google Scholar
[22] C. K. Kuo and W. X. Ma, “A study on resonant multi-soliton solutions to the (2+1)-dimensional Hirota-Satsuma-Ito equations via the linear superposition principle,” Nonlinear Anal., vol. 190, p. 111592, 2020. https://doi.org/10.1016/j.na.2019.111592.Suche in Google Scholar
[23] S. T. Chen and W. X. Ma, “Lump solutions of a generalized Calogero-Bogoyavlenskii-Schiff equation,” Comput. Math. Appl., vol. 76, pp. 1680–1685, 2018. https://doi.org/10.1016/j.camwa.2018.07.019.Suche in Google Scholar
[24] A. M. Wazwaz, “The (2+1) and (3+1)-dimensional CBS equations: multiple soliton solutions and multiple singular soliton solutions,” Z. Naturforsch., vol. 65A, pp. 173–181, 2010. https://doi.org/10.1515/zna-2010-0304.Suche in Google Scholar
[25] W. X. Ma, T. W. Huang, and Y. Zhang, “A multiple exp-function method for nonlinear differential equations and its application,” Phys. Scripta, vol. 82, p. 065003, 2010. https://doi.org/10.1088/0031-8949/82/06/065003.Suche in Google Scholar
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Artikel in diesem Heft
- Frontmatter
- Original Research Articles
- Modeling and assessment of the flow and air pollutants dispersion during chemical reactions from power plant activities
- Stochastic dynamics of dielectric elastomer balloon with viscoelasticity under pressure disturbance
- Unsteady MHD natural convection flow of a nanofluid inside an inclined square cavity containing a heated circular obstacle
- Fractional-order generalized Legendre wavelets and their applications to fractional Riccati differential equations
- Battery discharging model on fractal time sets
- Adaptive neural network control of second-order underactuated systems with prescribed performance constraints
- Optimal control for dengue eradication program under the media awareness effect
- Shifted Legendre spectral collocation technique for solving stochastic Volterra–Fredholm integral equations
- Modeling and simulations of a Zika virus as a mosquito-borne transmitted disease with environmental fluctuations
- Mathematical analysis of the impact of vaccination and poor sanitation on the dynamics of poliomyelitis
- Anti-sway method for reducing vibrations on a tower crane structure
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Stable soliton solutions to the time fractional evolution equations in mathematical physics via the new generalized
- Convergence analysis of online learning algorithm with two-stage step size
- An estimative (warning) model for recognition of pandemic nature of virus infections
- Interaction among a lump, periodic waves, and kink solutions to the KP-BBM equation
- Global exponential stability of periodic solution of delayed discontinuous Cohen–Grossberg neural networks and its applications
- An efficient class of fourth-order derivative-free method for multiple-roots
- Numerical modeling of thermal influence to pollutant dispersion and dynamics of particles motion with various sizes in idealized street canyon
- Construction of breather solutions and N-soliton for the higher order dimensional Caudrey–Dodd–Gibbon–Sawada–Kotera equation arising from wave patterns
- Delay-dependent robust stability analysis of uncertain fractional-order neutral systems with distributed delays and nonlinear perturbations subject to input saturation
- Construction of complexiton-type solutions using bilinear form of Hirota-type
- Inverse estimation of time-varying heat transfer coefficients for a hollow cylinder by using self-learning particle swarm optimization
- Infinite line of equilibriums in a novel fractional map with coexisting infinitely many attractors and initial offset boosting
- Lump solutions to a generalized nonlinear PDE with four fourth-order terms
- Quantum motion control for packaging machines
Artikel in diesem Heft
- Frontmatter
- Original Research Articles
- Modeling and assessment of the flow and air pollutants dispersion during chemical reactions from power plant activities
- Stochastic dynamics of dielectric elastomer balloon with viscoelasticity under pressure disturbance
- Unsteady MHD natural convection flow of a nanofluid inside an inclined square cavity containing a heated circular obstacle
- Fractional-order generalized Legendre wavelets and their applications to fractional Riccati differential equations
- Battery discharging model on fractal time sets
- Adaptive neural network control of second-order underactuated systems with prescribed performance constraints
- Optimal control for dengue eradication program under the media awareness effect
- Shifted Legendre spectral collocation technique for solving stochastic Volterra–Fredholm integral equations
- Modeling and simulations of a Zika virus as a mosquito-borne transmitted disease with environmental fluctuations
- Mathematical analysis of the impact of vaccination and poor sanitation on the dynamics of poliomyelitis
- Anti-sway method for reducing vibrations on a tower crane structure
-
Stable soliton solutions to the time fractional evolution equations in mathematical physics via the new generalized
- Convergence analysis of online learning algorithm with two-stage step size
- An estimative (warning) model for recognition of pandemic nature of virus infections
- Interaction among a lump, periodic waves, and kink solutions to the KP-BBM equation
- Global exponential stability of periodic solution of delayed discontinuous Cohen–Grossberg neural networks and its applications
- An efficient class of fourth-order derivative-free method for multiple-roots
- Numerical modeling of thermal influence to pollutant dispersion and dynamics of particles motion with various sizes in idealized street canyon
- Construction of breather solutions and N-soliton for the higher order dimensional Caudrey–Dodd–Gibbon–Sawada–Kotera equation arising from wave patterns
- Delay-dependent robust stability analysis of uncertain fractional-order neutral systems with distributed delays and nonlinear perturbations subject to input saturation
- Construction of complexiton-type solutions using bilinear form of Hirota-type
- Inverse estimation of time-varying heat transfer coefficients for a hollow cylinder by using self-learning particle swarm optimization
- Infinite line of equilibriums in a novel fractional map with coexisting infinitely many attractors and initial offset boosting
- Lump solutions to a generalized nonlinear PDE with four fourth-order terms
- Quantum motion control for packaging machines
