A (2 + 1)-dimensional variable-coefficients extension of the Date–Jimbo–Kashiwara–Miwa equation: Lie symmetry analysis, optimal system and exact solutions
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Yuru Hu
,
Feng Zhang
and
Hanze Liu
Abstract
In this article, the Date–Jimbo–Kashiwara–Miwa equation is extended to a new variable-coefficients equation with respect to the time variable. The infinitesimal generators are acquired by studying the Lie symmetry analysis of the equation, and the optimal system of this equation is presented. After that, the equation performed similarity reductions, and the reduced partial differential equations (PDEs) are transformed into ordinary differential equations (ODEs) with the help of traveling wave transform. Then, the exact solutions are found by applying the extended tanh-function method. Finally, the structural features of exact solutions to different times are shown with the help of images.
Funding source: National Natural Science Foundation of China
Award Identifier / Grant number: 11505090
Acknowledgments
This work is supported by the National Natural Science Foundation of China (Nos. 11505090), Research Award Foundation for Outstanding Young Scientists of Shandong Province (No. BS2015SF009) and the doctoral foundation of Liaocheng University under Grant No. 318051413, Liaocheng University level science and technology research fund No. 318012018.
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Author contributions: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
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Research funding: None declared.
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Conflict of interest statement: The authors declare no conflicts of interest regarding this article.
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© 2022 Walter de Gruyter GmbH, Berlin/Boston
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Articles in the same Issue
- Frontmatter
- Original Research Article
- Hybrid solitary wave solutions of the Camassa–Holm equation
- Numerical simulations of wave propagation in a stochastic partial differential equation model for tumor–immune interactions
- A Chebyshev collocation method for solving the non-linear variable-order fractional Bagley–Torvik differential equation
- Higher order codimension bifurcations in a discrete-time toxic-phytoplankton–zooplankton model with Allee effect
- Numerical modeling of the dam-break flood over natural rivers on movable beds
- A class of piecewise fractional functional differential equations with impulsive
- Lie symmetry analysis for two-phase flow with mass transfer
- Asymptotic behavior for stochastic plate equations with memory in unbounded domains
- Discussion on controllability of non-densely defined Hilfer fractional neutral differential equations with finite delay
- A linearized finite difference scheme for time–space fractional nonlinear diffusion-wave equations with initial singularity
- Ground state solutions of Schrödinger system with fractional p-Laplacian
- Bifurcation analysis of a new stochastic traffic flow model
- An uncertainty measure based on Pearson correlation as well as a multiscale generalized Shannon-based entropy with financial market applications
- Hilfer fractional stochastic evolution equations on infinite interval
- Iterative learning control for conformable stochastic impulsive differential systems with randomly varying trial lengths
- Chebyshev wavelet-Picard technique for solving fractional nonlinear differential equations
- Theoretical assessment of the impact of awareness programs on cholera transmission dynamic
- Theoretical and numerical analysis of a prey–predator model (3-species) in the frame of generalized Mittag-Leffler law
- Controllability discussion for fractional stochastic Volterra–Fredholm integro-differential systems of order 1 < r < 2
- Shehu transform on time-fractional Schrödinger equations – an analytical approach
- A (2 + 1)-dimensional variable-coefficients extension of the Date–Jimbo–Kashiwara–Miwa equation: Lie symmetry analysis, optimal system and exact solutions
- Mathematical model of fluid flow in a double constricted tapered tube with permeable boundary
