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New Solitary-Wave Solutions of the Van der Waals Normal Form for Granular Materials via New Auxiliary Equation Method

Author

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  • Xiaomeng Zhu

    (Hefei No. 8 High School, Hefei 230071, China
    Institute of Plasma Physics, Hefei Institutes of Physical Science, Chinese Academy of Sciences, Hefei 230031, China)

  • Jinkang Cheng

    (Hefei No. 8 High School, Hefei 230071, China
    Institute of Plasma Physics, Hefei Institutes of Physical Science, Chinese Academy of Sciences, Hefei 230031, China)

  • Zhuokai Chen

    (Hefei No. 8 High School, Hefei 230071, China
    Institute of Plasma Physics, Hefei Institutes of Physical Science, Chinese Academy of Sciences, Hefei 230031, China)

  • Guojiang Wu

    (Institute of Plasma Physics, Hefei Institutes of Physical Science, Chinese Academy of Sciences, Hefei 230031, China)

Abstract

In this paper, we use general Riccati equation to construct new solitary wave solutions of the Van der Waals normal form, which is one of the most famous models for natural and industrial granular materials. It is very important to understand the static and dynamic characteristics of this models in many application fields. We solve the general Riccati equation through different function transformation, and many new hyperbolic function solutions are obtained. Then, it is substituted into the Van der Waals normal form as an auxiliary equation. Abundant types of solitary-wave solutions are obtained by choosing different coefficient in the general Riccati equation, and some of them have not been found in other documents. The results show that the analysis method we used is very simple and effective for dealing with nonlinear models.

Suggested Citation

  • Xiaomeng Zhu & Jinkang Cheng & Zhuokai Chen & Guojiang Wu, 2022. "New Solitary-Wave Solutions of the Van der Waals Normal Form for Granular Materials via New Auxiliary Equation Method," Mathematics, MDPI, vol. 10(15), pages 1-16, July.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:15:p:2560-:d:869442
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    References listed on IDEAS

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    1. Seadawy, Aly R. & Lu, Dianchen & Nasreen, Naila & Nasreen, Shamila, 2019. "Structure of optical solitons of resonant Schrödinger equation with quadratic cubic nonlinearity and modulation instability analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 534(C).
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    Cited by:

    1. Feiyun Pei & Guojiang Wu & Yong Guo, 2023. "Construction of Infinite Series Exact Solitary Wave Solution of the KPI Equation via an Auxiliary Equation Method," Mathematics, MDPI, vol. 11(6), pages 1-25, March.

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