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Stability analysis and abundant closed-form wave solutions of the Date–Jimbo–Kashiwara–Miwa and combined sinh–cosh-Gordon equations arising in fluid mechanics

  • Aly R. Seadawy ORCID logo EMAIL logo and Asghar Ali
Published/Copyright: December 1, 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 manuscript, several types of exact solutions including trigonometric, hyperbolic, exponential, and rational function are successfully constructed with the implementation of two modified mathematical methods, namely called extended simple equation and modified F-expansion methods on the (2 + 1)-dimensional Date–Jimbo–Kashiwara–Miwa and the combined sinh–cosh-Gordon equations. Diverse form of solitary wave solutions is achieved from exact solutions by passing the special values to the parameters. Some solution are plotted in the form of 3D and 2D by assigning the specific values to parameters under the constrain condition to the solutions. These approaches yield the new solutions that we think other researchers have missed in the field of nonlinear sciences. Hence the searched wave’s results are loyal to the researchers and also have imperious applications in applied sciences.

Keywords: (2 + 1)-dimensional Date–Jimbo–Kashiwara–Miwa (DJKM) model; exact solutions; the combined sinh–cosh-Gordon equation mathematical methods
Corresponding author: Aly R. Seadawy, Mathematics Department, Faculty of Science, Taibah University, Al-Madinah Al-Munawarah, Saudi Arabia, 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: 2021-01-26
Accepted: 2021-11-04
Published Online: 2021-12-01

© 2021 Walter de Gruyter GmbH, Berlin/Boston

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https://doi.org/10.1515/ijnsns-2021-0033
Keywords for this article
(2 + 1)-dimensional Date–Jimbo–Kashiwara–Miwa (DJKM) model; exact solutions; the combined sinh–cosh-Gordon equation mathematical methods

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