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Comment on ‘two new integrable fourth-order nonlinear equations: multiple soliton solutions and multiple complex soliton solutions’

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Abstract

We comment on a recent paper by Wazwaz. We show that two fourth-order integrable nonlinear equations presented by him are related to the potential Ito equation by simple changes of variables.

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Data sharing not applicable to this article as no datasets were generated or analyzed during the current study.

References

  1. Wazwaz, A.M.: Two new integrable fourth-order nonlinear equations: multiple soliton solutions and multiple complex soliton solutions. Nonlinear Dyn. 94, 2655–2663 (2018)

    Article  Google Scholar 

  2. Baleanu, D., Alshomrani, A.S., Ullah, M.Z.: A new fourth-order integrable nonlinear equation: breather, rogue waves, other lump interaction phenomena, and conservation laws. Adv. Difference Equ. 2021, 195 (2021)

    Article  MathSciNet  Google Scholar 

  3. Ito, M.: An extension of nonlinear evolution equations of the Ito equation and a model equation for shallow water waves. J. Physic. Soc. Japan 49, 771–778 (1980)

    Article  Google Scholar 

  4. Drinfeld, V.G., Sokolov, V.V.: New evolutionary equations possessing an (L, A)-pair (in Russian). Proc. S. L. Sobolev Seminar Novosibirsk 2, 5–9 (1981)

    Google Scholar 

  5. Hu, X.B., Li, Y.: Nonlinear superposition formulae of the Ito equation and a model equation for shallow water waves. J. Phys. A: Math. Gen. 24, 1979–1986 (1999)

    Article  MathSciNet  Google Scholar 

  6. Liu, Q.P.: Hamiltonian structures of Ito‘s equation. Phys. Lett. A 277, 31–34 (2000)

    Article  MathSciNet  Google Scholar 

  7. Niu, X.X., Zhang, M.X., Lv, S.Q.: A Darboux Transformation for Ito Equation. Zeitschrift für Naturforschung A 71, 427–431 (2016)

    Article  Google Scholar 

  8. Hu, X., Shen, S., Jin, Y.: Rogue wave and interaction phenomenon to (1+1)-dimensional Ito equation. Appl. Math. Lett. 90, 99–103 (2018)

    Article  MathSciNet  Google Scholar 

  9. Hu, X., Lin, S., Shen, S.: New interaction solutions to (1+1)-dimensional Ito equation. Appl. Math. Lett. 101, 106071 (2020)

    Article  MathSciNet  Google Scholar 

  10. Zhang, Y.N., Chang, X.K., Hu, J., Hu, X.B., Tam, H.W.: Integrable discretization of soliton equations via bilinear method and Bäcklund transformation. Sci. China Math. 58, 279–296 (2015)

    Article  MathSciNet  Google Scholar 

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Acknowledgements

We would like to thank Prof. Q. P. Liu for interesting discussions, and anonymous referees for helpful comments. This work is supported by the National Natural Science Foundation of China (Grant Nos. 11871471 and 11931017).

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Correspondence to Mengxia Zhang.

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Tian, Y., Zhang, M. Comment on ‘two new integrable fourth-order nonlinear equations: multiple soliton solutions and multiple complex soliton solutions’. Nonlinear Dyn 107, 3175–3176 (2022). https://doi.org/10.1007/s11071-021-07035-5

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  • DOI: https://doi.org/10.1007/s11071-021-07035-5

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