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One-dimensional optimal system and similarity transformations for the 3 + 1 Kudryashov–Sinelshchikov equation

  • Andronikos Paliathanasis ORCID logo EMAIL logo
Published/Copyright: November 23, 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 3

Abstract

We apply the Lie theory to determine the infinitesimal generators of the one-parameter point transformations which leave invariant the 3 + 1 Kudryashov–Sinelshchikov equation. We solve the classification problem of the one-dimensional optimal system, while we derive all the possible independent Lie invariants; that is, we determine all the independent similarity transformations which lead to different reductions. For an application, the results are applied to prove the existence of travel-wave solutions. Furthermore, the method of singularity analysis is applied where we show that the 3 + 1 Kudryashov–Sinelshchikov equation possess the Painlevé property and its solution can be written by using a Laurent expansion.

Keywords: Kudryashov–Sinelshchikov equation; Lie symmetries; nonlinear waves; optimal system
Corresponding author: Andronikos Paliathanasis, Institute of Systems Science, Durban University of Technology, P.O. Box 1334, Durban 4000, Republic of South Africa; and Instituto de Ciencias Físicas y Matemáticas, Universidad Austral de Chile, Valdivia, Chile, E-mail:

  1. Author contributions: 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: 2020-09-29
Accepted: 2021-11-04
Published Online: 2021-11-23

© 2021 Walter de Gruyter GmbH, Berlin/Boston

Articles in the same Issue

  1. Frontmatter
  2. Original Research Articles
  3. One-dimensional optimal system and similarity transformations for the 3 + 1 Kudryashov–Sinelshchikov equation
  4. Hopf bifurcations in a network of FitzHugh–Nagumo biological neurons
  5. Gravity modulation effect on weakly nonlinear thermal convection in a fluid layer bounded by rigid boundaries
  6. A new numerical formulation for the generalized time-fractional Benjamin Bona Mohany Burgers’ equation
  7. Chebyshev spectral method for solving a class of local and nonlocal elliptic boundary value problems
  8. Adaptive extragradient methods for solving variational inequalities in real Hilbert spaces
  9. Elastic trend filtering
  10. A new approach to representations of homothetic motions in Lorentz space
  11. Numerical simulation of variable-order fractional differential equation of nonlinear Lane–Emden type appearing in astrophysics
  12. Stability analysis and numerical simulations of the fractional COVID-19 pandemic model
  13. Numerical solutions of the Bagley–Torvik equation by using generalized functions with fractional powers of Laguerre polynomials
  14. N-fold Darboux transformation and exact solutions for the nonlocal Fokas–Lenells equation on the vanishing and plane wave backgrounds
  15. Closed form soliton solutions to the space-time fractional foam drainage equation and coupled mKdV evolution equations
  16. Master-slave synchronization in the Duffing-van der Pol and Φ6 Duffing oscillators
  17. Singularity analysis and analytic solutions for the Benney–Gjevik equations
  18. Trajectory controllability of nonlinear fractional Langevin systems
  19. Similarity transformations for modified shallow water equations with density dependence on the average temperature
  20. Non-equidistant partition predictor–corrector method for fractional differential equations with exponential memory
  21. Dynamical analysis of fractional-order of IVGTT glucose–insulin interaction
  22. Dynamic response of Mathieu–Duffing oscillator with Caputo derivative
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  24. A class of computationally efficient Newton-like methods with frozen inverse operator for nonlinear systems
https://doi.org/10.1515/ijnsns-2020-0219
Keywords for this article
Kudryashov–Sinelshchikov equation; Lie symmetries; nonlinear waves; optimal system

Articles in the same Issue

  1. Frontmatter
  2. Original Research Articles
  3. One-dimensional optimal system and similarity transformations for the 3 + 1 Kudryashov–Sinelshchikov equation
  4. Hopf bifurcations in a network of FitzHugh–Nagumo biological neurons
  5. Gravity modulation effect on weakly nonlinear thermal convection in a fluid layer bounded by rigid boundaries
  6. A new numerical formulation for the generalized time-fractional Benjamin Bona Mohany Burgers’ equation
  7. Chebyshev spectral method for solving a class of local and nonlocal elliptic boundary value problems
  8. Adaptive extragradient methods for solving variational inequalities in real Hilbert spaces
  9. Elastic trend filtering
  10. A new approach to representations of homothetic motions in Lorentz space
  11. Numerical simulation of variable-order fractional differential equation of nonlinear Lane–Emden type appearing in astrophysics
  12. Stability analysis and numerical simulations of the fractional COVID-19 pandemic model
  13. Numerical solutions of the Bagley–Torvik equation by using generalized functions with fractional powers of Laguerre polynomials
  14. N-fold Darboux transformation and exact solutions for the nonlocal Fokas–Lenells equation on the vanishing and plane wave backgrounds
  15. Closed form soliton solutions to the space-time fractional foam drainage equation and coupled mKdV evolution equations
  16. Master-slave synchronization in the Duffing-van der Pol and Φ6 Duffing oscillators
  17. Singularity analysis and analytic solutions for the Benney–Gjevik equations
  18. Trajectory controllability of nonlinear fractional Langevin systems
  19. Similarity transformations for modified shallow water equations with density dependence on the average temperature
  20. Non-equidistant partition predictor–corrector method for fractional differential equations with exponential memory
  21. Dynamical analysis of fractional-order of IVGTT glucose–insulin interaction
  22. Dynamic response of Mathieu–Duffing oscillator with Caputo derivative
  23. Non-Newtonian fluid flow having fluid–particle interaction through a porous zone in a channel with permeable walls
  24. A class of computationally efficient Newton-like methods with frozen inverse operator for nonlinear systems
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