Research Article

New Traveling Wave Solutions for the Sixth-order Boussinesq Equation

Volume: 6 Number: 1 March 29, 2023
EN

New Traveling Wave Solutions for the Sixth-order Boussinesq Equation

Abstract

In this paper, we investigate the new traveling wave solutions for the sixth-order Boussinesq equation using the tanh-coth method. Such a method is a type of expansion method that represents the solutions of partial differential equations as polynomials of $\tanh$ and $\coth$ functions. We discover several new traveling wave solutions for the sixth-order Boussinesq equation with different parameters, which are of fundamental importance for various applications.

Keywords

References

  1. [1] J. Boussinesq, Theorie de I’intumescence liquide, applelee onde solitaire ou de translation, se propageant dans un canal rectangulaire, C. R. Acad. Sci., 72 (1871), 755-759.
  2. [2] J. Boussinesq, Theorie des ondes et des remous qui se progagent le long d’un canal rectangulaire horizontal, en communiquant au liquide contenu dans ce canal des vitesses sensiblement pareilles de la surface au fond, J. Math. Pures Appl., 17 (1872), 55-108.
  3. [3] J. Zhou, H. Zhang, Well-posedness of solutions for the sixth-order Boussinesq equation with linear strong damping and nonlinear source, J. Nonlinear Sci., 31 (2021), 1-61.
  4. [4] J. Liu, X. Wang, J. Zhou, H. Zhang, Blow-up phenomena for the sixth-order Boussinesq equation with fourth-order dispersion term and nonlinear source, Discrete Contin. Dyn. Syst. - S, 14 (2021), 4321-4335.
  5. [5] H. Wang, A. Esfahani, Global rough solutions to the sixth-order Boussinesq equation, Nonlinear Anal. Theory Methods Appl., 102 (2014), 97-104.
  6. [6] H. Yang, An inverse problem for the sixth-order linear Boussinesq-type equation, UPB Sci. Bull. A: Appl. Math. Phys., 82 (2020), 27-36.
  7. [7] C.I. Christov, G.A. Maugin, M.G. Velarde, Well-posed Boussinesq paradigm with purely spatial higher-order derivatives, Phys. Rev. E, 54 (1996), 3621-3638.
  8. [8] S. Li, M. Chen, B.Y. Zhang, Exact controllability and stability of the sixth order Boussinesq equation, (2018), arXiv:1811.05943 [math.AP].

Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Publication Date

March 29, 2023

Submission Date

July 15, 2022

Acceptance Date

November 17, 2022

Published in Issue

Year 2023 Volume: 6 Number: 1

APA
Yang, H. (2023). New Traveling Wave Solutions for the Sixth-order Boussinesq Equation. Fundamental Journal of Mathematics and Applications, 6(1), 1-11. https://doi.org/10.33401/fujma.1144277
AMA
1.Yang H. New Traveling Wave Solutions for the Sixth-order Boussinesq Equation. Fundam. J. Math. Appl. 2023;6(1):1-11. doi:10.33401/fujma.1144277
Chicago
Yang, He. 2023. “New Traveling Wave Solutions for the Sixth-Order Boussinesq Equation”. Fundamental Journal of Mathematics and Applications 6 (1): 1-11. https://doi.org/10.33401/fujma.1144277.
EndNote
Yang H (March 1, 2023) New Traveling Wave Solutions for the Sixth-order Boussinesq Equation. Fundamental Journal of Mathematics and Applications 6 1 1–11.
IEEE
[1]H. Yang, “New Traveling Wave Solutions for the Sixth-order Boussinesq Equation”, Fundam. J. Math. Appl., vol. 6, no. 1, pp. 1–11, Mar. 2023, doi: 10.33401/fujma.1144277.
ISNAD
Yang, He. “New Traveling Wave Solutions for the Sixth-Order Boussinesq Equation”. Fundamental Journal of Mathematics and Applications 6/1 (March 1, 2023): 1-11. https://doi.org/10.33401/fujma.1144277.
JAMA
1.Yang H. New Traveling Wave Solutions for the Sixth-order Boussinesq Equation. Fundam. J. Math. Appl. 2023;6:1–11.
MLA
Yang, He. “New Traveling Wave Solutions for the Sixth-Order Boussinesq Equation”. Fundamental Journal of Mathematics and Applications, vol. 6, no. 1, Mar. 2023, pp. 1-11, doi:10.33401/fujma.1144277.
Vancouver
1.He Yang. New Traveling Wave Solutions for the Sixth-order Boussinesq Equation. Fundam. J. Math. Appl. 2023 Mar. 1;6(1):1-11. doi:10.33401/fujma.1144277

Cited By

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