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Bifurcations and exact soliton solutions for generalized Dullin–Gottwald–Holm equation with cubic power law nonlinearity

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Abstract

In this paper, we study a system of generalized Dullin–Gottwald–Holm equation with cubic power law nonlinearity. With bifurcation method of dynamical system, we obtain bifurcation of generalized Dullin–Gottwald–Holm equation with Cubic Power Law Nonlinearity. Unfortunately, Hamilton function is a quintic hyper-elliptic function, and it is very difficulty to calculate the integral of the Hamilton function. With the help of Grobner basis elimination method, the modified simplest equation method, and Maple software, we obtain some useful traveling wave solution, including kink wave solutions, anti-kink wave solutions and singular wave solutions. These conclusions may complement and improve previous conclusions. These solutions may help us to understand mechanisms of complex physical phenomena and dynamical processes.

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Availability of data and material

The data generated during the current study are available from the corresponding author on reasonable request.

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Funding

The paper partly funded by the Science and Technology Project of Education Department of Jiangxi Province(No.GJJ191645).

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Authors and Affiliations

  1. South China Business College, Guangdong University of Foreign Studies, Guangzhou, 510545, China

    Deniu Yang

  2. Nanchang Normal College of Applied Technology, Nanchang, 330000, China

    Quanfu Lou

  3. Jiangxi Vocational College of Mechanical & Electrical Technology, Nanchang, 330000, China

    Juan Zhang

Authors
  1. Deniu Yang
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  2. Quanfu Lou
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  3. Juan Zhang
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Corresponding author

Correspondence to Deniu Yang.

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The authors declare that they have no conflict of interest.

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The codes generated during the current study are available from the corresponding author on reasonable request.

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Yang, D., Lou, Q. & Zhang, J. Bifurcations and exact soliton solutions for generalized Dullin–Gottwald–Holm equation with cubic power law nonlinearity. Eur. Phys. J. Plus 137, 240 (2022). https://doi.org/10.1140/epjp/s13360-022-02462-8

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  • DOI: https://doi.org/10.1140/epjp/s13360-022-02462-8

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