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Lump solutions to a generalized nonlinear PDE with four fourth-order terms

  • Qingxian Chen ORCID logo , Wen-Xiu Ma EMAIL logo and Yehui Huang
Published/Copyright: May 16, 2022
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International Journal of Nonlinear Sciences and Numerical Simulation
From the journal International Journal of Nonlinear Sciences and Numerical Simulation Volume 24 Issue 1

Abstract

A combined fourth-order (2 + 1)-dimensional nonlinear partial differential equation which contains four fourth-order nonlinear terms and all second-order linear terms is formulated. This equation covers three generalized KP, Hirota–Satsuma–Ito, and Calogero–Bogoyavlenskii–Schiff equations as examples, which have physical applications in the study of various nonlinear phenomena in nature. In terms of some settings of the coefficients, a class of lump solutions is constructed by the Hirota bilinear method and the solutions are calculated through the symbolic computation system of Maple. Meanwhile, the relation between the coefficients and the solution is explored. Two special lump solutions are generated by taking proper values for the involved coefficients and parameters, and their dynamic behaviors are studied, as illustrative examples. The primary advantage of the Hirota bilinear method is to transform a nonlinear equation into a bilinear one so that the targeted equation can be easily studied.

Keywords: Hirota bilinear method; lump solution; soliton; symbolic computation
PACS numbers: 02.30.IK
Corresponding author: Wen-Xiu Ma, Department of Mathematics, Zhejiang Normal University, Jinhua 321004, Zhejiang, PR China; Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia; School of Mathematical and Statistical Sciences, North-West University, Mafikeng Campus, Private Bag X2046, Mmabatho 2735, South Africa; Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620, USA; and College of Mathematics and Physics, Shanghai University of Electric Power, Shanghai 200090, PR China, E-mail:

Funding source: National Natural Science Foundation of China

Award Identifier / Grant number: 11975145 and 11972291

Funding source: Fundamental Research Funds of the Central Universities

Award Identifier / Grant number: 2020MS043

Funding source: The National Natural Science Foundation of China

Award Identifier / Grant number: 12171475

Funding source: Beijing Natural Science Foundation

Award Identifier / Grant number: Z200001

Funding source: The Ministry of Science and Technology of China

Award Identifier / Grant number: G2021016032L

  1. Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: This work is supported in part by the Fundamental Research Funds of the Central Universities with the [grant number 2020MS043], the National Natural Science Foundation of China (grant number 12171475), Beijing Natural Science Foundation (grant number Z200001), the Ministry of Science and Technology of China (grant number G2021016032L) and the National Natural Science Foundation of China [grant number 11975145 and 11972291].

  3. Conflict of interest statement: The authors declare that they have no conflict of interest.

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Received: 2020-08-05
Accepted: 2022-04-18
Published Online: 2022-05-16
Published in Print: 2023-02-23

© 2022 Walter de Gruyter GmbH, Berlin/Boston

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https://doi.org/10.1515/ijnsns-2020-0183
Keywords for this article
Hirota bilinear method; lump solution; soliton; symbolic computation

Articles in the same Issue

  1. Frontmatter
  2. Original Research Articles
  3. Modeling and assessment of the flow and air pollutants dispersion during chemical reactions from power plant activities
  4. Stochastic dynamics of dielectric elastomer balloon with viscoelasticity under pressure disturbance
  5. Unsteady MHD natural convection flow of a nanofluid inside an inclined square cavity containing a heated circular obstacle
  6. Fractional-order generalized Legendre wavelets and their applications to fractional Riccati differential equations
  7. Battery discharging model on fractal time sets
  8. Adaptive neural network control of second-order underactuated systems with prescribed performance constraints
  9. Optimal control for dengue eradication program under the media awareness effect
  10. Shifted Legendre spectral collocation technique for solving stochastic Volterra–Fredholm integral equations
  11. Modeling and simulations of a Zika virus as a mosquito-borne transmitted disease with environmental fluctuations
  12. Mathematical analysis of the impact of vaccination and poor sanitation on the dynamics of poliomyelitis
  13. Anti-sway method for reducing vibrations on a tower crane structure
  14. Stable soliton solutions to the time fractional evolution equations in mathematical physics via the new generalized G ′ / G -expansion method
  15. Convergence analysis of online learning algorithm with two-stage step size
  16. An estimative (warning) model for recognition of pandemic nature of virus infections
  17. Interaction among a lump, periodic waves, and kink solutions to the KP-BBM equation
  18. Global exponential stability of periodic solution of delayed discontinuous Cohen–Grossberg neural networks and its applications
  19. An efficient class of fourth-order derivative-free method for multiple-roots
  20. Numerical modeling of thermal influence to pollutant dispersion and dynamics of particles motion with various sizes in idealized street canyon
  21. Construction of breather solutions and N-soliton for the higher order dimensional Caudrey–Dodd–Gibbon–Sawada–Kotera equation arising from wave patterns
  22. Delay-dependent robust stability analysis of uncertain fractional-order neutral systems with distributed delays and nonlinear perturbations subject to input saturation
  23. Construction of complexiton-type solutions using bilinear form of Hirota-type
  24. Inverse estimation of time-varying heat transfer coefficients for a hollow cylinder by using self-learning particle swarm optimization
  25. Infinite line of equilibriums in a novel fractional map with coexisting infinitely many attractors and initial offset boosting
  26. Lump solutions to a generalized nonlinear PDE with four fourth-order terms
  27. Quantum motion control for packaging machines
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