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The (3 + 1)-dimensional Wazwaz–KdV equations: the conservation laws and exact solutions

  • Arzu Akbulut ORCID logo EMAIL logo , Hadi Rezazadeh , Mir Sajjad Hashemi ORCID logo and Filiz Taşcan
Published/Copyright: November 26, 2021
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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 2

Abstract

In this study, we dealt with the new conservation theorem and the auxiliary method. We have applied the theorem and method to (3 + 1)-dimensional modified Wazwaz–KdV equations. When we applied a new conservation theorem to given equations, the obtained conservation laws did not satisfy the divergence condition. So, we modified the obtained conservation laws. These conservation laws contain extra terms. Finally, we applied the auxiliary method to given equations. We obtained two solution families with six exact solutions. All the obtained solutions are different from each other. For a suitable value of the solutions, the 3D and 2D surfaces have been plotted by Maple.

Keywords: (3 + 1)-dimensional modified Wazwaz–KdV equations; auxiliary method; exact solutions; new conservation theorem
PACS (2010): 02.30 Jr; 02.70 Wz; 94.05 Fg; 11.30.-j
Corresponding author: Arzu Akbulut, Department of Mathematics – Computer, Eskişehir Osmangazi University, Art-Science Faculty, Eskişehir, Türkiye, E-mail:

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

  2. Research funding: None declared.

  3. Conflict of interest statement: The authors declare no conflicts of interest regarding this article.

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Received: 2021-04-14
Revised: 2021-08-05
Accepted: 2021-11-04
Published Online: 2021-11-26

© 2021 Walter de Gruyter GmbH, Berlin/Boston

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https://doi.org/10.1515/ijnsns-2021-0161
Keywords for this article
(3 + 1)-dimensional modified Wazwaz–KdV equations; auxiliary method; exact solutions; new conservation theorem

Articles in the same Issue

  1. Frontmatter
  2. Original Research Articles
  3. Numerical solutions for variable-order fractional Gross–Pitaevskii equation with two spectral collocation approaches
  4. Threshold dynamics of an HIV-1 model with both virus-to-cell and cell-to-cell transmissions, immune responses, and three delays
  5. Numerical scheme and analytical solutions to the stochastic nonlinear advection diffusion dynamical model
  6. On modeling column crystallizers and a Hermite predictor–corrector scheme for a system of integro-differential equations
  7. On a discrete fractional stochastic Grönwall inequality and its application in the numerical analysis of stochastic FDEs involving a martingale
  8. A new self adaptive Tseng’s extragradient method with double-projection for solving pseudomonotone variational inequality problems in Hilbert spaces
  9. Solitary waves of the RLW equation via least squares method
  10. Optical solitons and stability regions of the higher order nonlinear Schrödinger’s equation in an inhomogeneous fiber
  11. Weighted pseudo asymptotically Bloch periodic solutions to nonlocal Cauchy problems of integrodifferential equations in Banach spaces
  12. Modified inertial subgradient extragradient method for equilibrium problems
  13. Propagation of dark-bright soliton and kink wave solutions of fluidized granular matter model arising in industrial applications
  14. Existence and uniqueness of positive solutions for fractional relaxation equation in terms of ψ-Caputo fractional derivative
  15. Investigation of nonlinear fractional delay differential equation via singular fractional operator
  16. Travelling peakon and solitary wave solutions of modified Fornberg–Whitham equations with nonhomogeneous boundary conditions
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  18. Stability and ψ-algebraic decay of the solution to ψ-fractional differential system
  19. Some new characterizations of a space curve due to a modified frame N ⃗ , C ⃗ , W ⃗ in Euclidean 3-space
  20. Numerical simulation of particulate matter propagation in an indoor environment with various types of heating
  21. Inertial accelerated algorithms for solving split feasibility with multiple output sets in Hilbert spaces
  22. Stability analysis and abundant closed-form wave solutions of the Date–Jimbo–Kashiwara–Miwa and combined sinh–cosh-Gordon equations arising in fluid mechanics
  23. Contrasting effects of prey refuge on biodiversity of species
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