An Extension to Direct Method of Clarkson and Kruskal and Painlev$$\acute{e}$$ Analysis for the System of Variable Coefficient Nonlinear Partial Differential Equations

Gupta, Rajesh Kumar; Sharma, Manjeet

doi:10.1007/s12346-024-00994-1

Qual. Theory Dyn. Syst.

2024

DOI: 10.1007/s12346-024-00994-1

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An Extension to Direct Method of Clarkson and Kruskal and Painlev$$\acute{e}$$ Analysis for the System of Variable Coefficient Nonlinear Partial Differential Equations

Rajesh Kumar Gupta,

Manjeet Sharma

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Cited by 2 publications

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Lie-bäcklund symmetry, soliton solutions, chaotic structure and its characteristics of the extended (3 + 1) dimensional Kairat-II model

Almheidat,

Alqudah,

Alderremy

et al. 2024

Nonlinear Dyn

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This study investigates the (3 + 1)-dimensional extended Kairat-II model using Lie-Bäcklund symmetry (LBS) and the improved modified extended tanh-function approach (IMETFA). The bifurcation and sensitivity analyses are conducted to understand the stability and chaotic behavior of the model. Through graphical visualizations of phase diagrams, Lyapunov exponents, power spectra, fractal dimension and recurrence plots, the complex dynamics and stability characteristics of the model are elucidated. Additionally, the research focuses on the derivation of dark soliton and various combo soliton solutions of the Kairat-II model. The derived soliton solutions are graphically displayed in 3D and 2D plots. The obtained results are new and have never been reported in the literature for the considered equation.

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Lie-bäcklund symmetry, soliton solutions, chaotic structure and its characteristics of the extended (3 + 1) dimensional Kairat-II model

Almheidat,

Alqudah,

Alderremy

et al. 2024

Nonlinear Dyn

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show abstract

Auto-Bäcklund Transformation with the Solitons and Similarity Reductions for a Generalized Nonlinear Shallow Water Wave Equation

Gao

2024

Qual. Theory Dyn. Syst.

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An Extension to Direct Method of Clarkson and Kruskal and Painlev$$\acute{e}$$ Analysis for the System of Variable Coefficient Nonlinear Partial Differential Equations

Cited by 2 publications

References 47 publications

Lie-bäcklund symmetry, soliton solutions, chaotic structure and its characteristics of the extended (3 + 1) dimensional Kairat-II model

Lie-bäcklund symmetry, soliton solutions, chaotic structure and its characteristics of the extended (3 + 1) dimensional Kairat-II model

Auto-Bäcklund Transformation with the Solitons and Similarity Reductions for a Generalized Nonlinear Shallow Water Wave Equation

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