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Application of the modified Kudryashov method to the generalized Schrödinger–Boussinesq equations

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Abstract

In the paper, the modified Kudryashov method is applied to find new exact solutions for the generalized Schrödinger–Boussinesq equation with the help of symbolic computation package Maple through the complex transform. The obtained solutions have been checked by substituting back into its corresponding equation with the aid of Maple package program.

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References

  • Akbulut, A., Kaplan, M.: Auxiliary equation method for time-fractional differential equations with conformable derivative. Comput. Math Appl. 75(3), 876–882 (2017). https://doi.org/10.1016/j.camwa.2017.10.016

    Article  MathSciNet  Google Scholar 

  • Bai, C.-L.: Exact solutions for nonlinear partial differential equation: a new approach. Phys. Lett. A 288(3), 191–195 (2001)

    Article  ADS  MathSciNet  Google Scholar 

  • Bilige, S., Sudao, C., Chaolu, C., Wang, X.: Application of the extended simplest equation method to the coupled Schrödinger–Boussinesq equation. Appl. Math. Comput. 224, 517–523 (2013)

    MathSciNet  MATH  Google Scholar 

  • Chanda, P.K., Chowdhury, A.R.: On a Painlevé test of a coupled system of Boussinesq and Schrödinger equations. J. Math. Phys. 29(4), 843–850 (1988)

    Article  ADS  MathSciNet  Google Scholar 

  • Chowdhury, A.R., Rao, N.N.: Painléve analysis and backlund transformations for coupled generalized Schrödinger–Boussinesq system. Chaos Solitons Fractals 9(10), 1747–1753 (1998)

    Article  ADS  MathSciNet  Google Scholar 

  • Deng, X.: Exact solitary and periodic wave solutions for the coupled Schrödinger–Boussinesq equation. Optik 136, 312–318 (2017)

    Article  ADS  Google Scholar 

  • Eslami, M.: Soliton-like solutions for the coupled Schrödinger–Boussinesq equation. Optik 126(23), 3987–3991 (2015)

    Article  ADS  Google Scholar 

  • Gepreel, A.K.: Extended trial equation method for nonlinear coupled Schrödinger–Boussinesq partial differential equations. J. Egypt. Math. Soc. 24(3), 381–391 (2016)

    Article  MathSciNet  Google Scholar 

  • Hon, Y.C., Fan, E.G.: A series of exact solutions for coupled Higgs field equation and coupled Schrödinger–Boussinesq equation. Nonlinear Anal. Theor. Methods Appl. 71(7), 3501–3508 (2009)

    Article  Google Scholar 

  • Hong, B., Lu, D.: New exact Jacobi elliptic function solutions for the coupled Schrödinger-Boussinesq equations. J. Appl. Math. (2013). https://doi.org/10.1155/2013/170835

    Article  Google Scholar 

  • Huang, X.: The investigation of solutions to the coupled Schrödinger-Boussinesq equations. Abstr. Appl. Anal. (2013). https://doi.org/10.1155/2013/170372

    Article  MATH  Google Scholar 

  • Jiang, M., Dai, Z.: Various Heteroclinic Solutions for the Coupled Schrödinger-Boussinesq Equation. Abstr. Appl. Anal. (2013). https://doi.org/10.1155/2013/158140

    Article  MATH  Google Scholar 

  • Kaplan, M., Bekir, A.: A novel analytical method for time-fractional differential equations. Optik 127, 8209–8214 (2016a)

    Article  ADS  Google Scholar 

  • Kaplan, M., Bekir, A.: The modified simple equation method for solving some fractional-order nonlinear equations. Pramana 87(1), 1–5 (2016b)

    Article  Google Scholar 

  • Khater, M.M.A., Kumar, D.: Implementation of three reliable methods for finding the exact solutions of (2 + 1) dimensional generalized fractional evolution equations. Opt. Quantum Electron. 49, 427 (2017). https://doi.org/10.1007/s11082-017-1249-3

    Article  Google Scholar 

  • Khater, M.M.A., Seadawy, A.R., Lu, D.: Dispersive optical soliton solutions for higher order nonlinear Sasa-Satsuma equation in mono mode fibers via new auxiliary equation method. Superlattices Microstruct. 113, 346–358 (2017). https://doi.org/10.1016/j.spmi.2017.11.011

    Article  ADS  Google Scholar 

  • Kumar, D., Hosseini, K., Samadani, F.: The sine-Gordon expansion method to look for the traveling wave solutions of the Tzitzéica type equations in nonlinear optics. Optik 149, 439–446 (2017)

    Article  ADS  Google Scholar 

  • Kumar, D., Manafian, J., Hawlader, F., Ranjbaran, A.: New closed form soliton and other solutions of the Kundu-Eckhaus equation via the extended sinh-Gordon equation expansion method. Optik 160, 159–167 (2018a)

    Article  ADS  Google Scholar 

  • Kumar, D., Seadawy, A.R., Chowdhury, R.: On new complex soliton structures of the nonlinear partial differential equations describing the pulse narrowing nonlinear transmission lines. Opt. Quantum Electron. 50(2), 108 (2018b)

    Article  Google Scholar 

  • Kumar, D., Seadawy, A.R., Joardar, A.K.: Modified Kudryashov method via new exact solutions for some conformable fractional differential equations arising in mathematical biology. Chin. J. Phys. 56(1), 75–85 (2018c)

    Article  Google Scholar 

  • Kumar, D., Darvishi, M.T., Joardar, A.K.: Modified Kudryashov method and its application to the fractional version of the variety of Boussinesq-like equations in shallow water. Opt. Quantum Electron. 50(3), 128 (2018d)

    Article  Google Scholar 

  • Li, Z.: Heteroclinic breather-wave for the coupled Schrödinger–Boussinesq equation. Appl. Math. Sci. 8(120), 5995–6000 (2014)

    Google Scholar 

  • Li, W., Yomba, E., Zhang, H.: New exact solutions for some coupled nonlinear partial differential equations using extended coupled sub-equations expansion method. Appl. Math. Comput. 217(21), 8468–8481 (2011)

    MathSciNet  MATH  Google Scholar 

  • Manafian, J., Aghdaei, M.F.: Abundant soliton solutions for the coupled Schrödinger–Boussinesq system via an analytical method. Eur. Phys. J. Plus 131, 97 (2016). https://doi.org/10.1140/epjp/i2016-16097-3

    Article  Google Scholar 

  • Neirameh, A.: Topological soliton solutions to the coupled Schrödinger–Boussinesq equation by the SEM. Optik 126(23), 4179–4183 (2015)

    Article  ADS  Google Scholar 

  • Ray, S.S.: New double periodic exact solutions of the coupled Schrödinger-Boussinesq equations describing physical processes in laser and plasma physics. Chin. J. Phys. 55(5), 2039–2047 (2017)

    Article  Google Scholar 

  • Wang, H., Chen, L., Liu, H.: Exact solutions of travelling wave model via dynamical system method. Abstr. Appl. Anal. 2016, 7 (2016)

    Article  MathSciNet  Google Scholar 

  • Yang, X., Zhao, C., Cao, J.: Dynamics of the discrete coupled nonlinear Schrödinger–Boussinesq equations. Appl. Math. Comput. 219(16), 8508–8524 (2013)

    MathSciNet  MATH  Google Scholar 

  • Zayed, E.M.E., Alurrfi, K.A.E.: On solving the nonlinear Schrödinger–Boussinesq equation and the hyperbolic Schrödinger equation by using the (G′/G, 1/G)-expansion method. Int. J. Phys. Sci. 9(19), 415–429 (2014)

    Article  Google Scholar 

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Authors and Affiliations

  1. Graduate School of Systems and Information Engineering, University of Tsukuba, Tennodai 1-1-1, Tsukuba, Ibaraki, Japan

    Dipankar Kumar

  2. Department of Mathematics, Bangabandhu Sheikh Mujibur Rahman Science and Technology University, Gopalganj, 8100, Bangladesh

    Dipankar Kumar

  3. Department of Mathematics, Art-Science Faculty, Kastamonu University, Kastamonu, Turkey

    Melike Kaplan

Authors
  1. Dipankar Kumar
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  2. Melike Kaplan
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Correspondence to Melike Kaplan.

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Kumar, D., Kaplan, M. Application of the modified Kudryashov method to the generalized Schrödinger–Boussinesq equations. Opt Quant Electron 50, 329 (2018). https://doi.org/10.1007/s11082-018-1595-9

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  • DOI: https://doi.org/10.1007/s11082-018-1595-9

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