| Citation: |
Turgut Ak, Mohammed S. Osman, Abdul Hamid Kara. POLYNOMIAL AND RATIONAL WAVE SOLUTIONS OF KUDRYASHOV-SINELSHCHIKOV EQUATION AND NUMERICAL SIMULATIONS FOR ITS DYNAMIC MOTIONS[J]. Journal of Applied Analysis & Computation, 2020, 10(5): 2145-2162. doi: 10.11948/20190341
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POLYNOMIAL AND RATIONAL WAVE SOLUTIONS OF KUDRYASHOV-SINELSHCHIKOV EQUATION AND NUMERICAL SIMULATIONS FOR ITS DYNAMIC MOTIONS
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Abstract
Polynomial and rational wave solutions of Kudryashov-Sinelshchikov equation and numerical simulations for its dynamic motions are investigated. Conservation flows of the dynamic motion are obtained utilizing multiplier approach. Using the unified method, a collection of exact solitary and soliton solutions of Kudryashov-Sinelshchikov equation is presented. Collocation finite element method based on quintic B-spline functions is implemented to the equation to evidence the accuracy of the proposed method by test problems. Stability analysis of the numerical scheme is studied by employing von Neumann theory. The obtained analytical and numerical results are in good agreement. -
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References
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Turgut Ak, Mohammed S. Osman, Abdul Hamid Kara. POLYNOMIAL AND RATIONAL WAVE SOLUTIONS OF KUDRYASHOV-SINELSHCHIKOV EQUATION AND NUMERICAL SIMULATIONS FOR ITS DYNAMIC MOTIONS[J]. Journal of Applied Analysis & Computation, 2020, 10(5): 2145-2162. doi: 10.11948/20190341
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Figure 1. Solitary wave solution of Eq.
$ (1.1) $ for$ \alpha=2 $ ,$ \beta=1 $ ,$ \gamma=0.1 $ ,$ \kappa=1 $ , and$ \mu=0.5 $ . -
Figure 2. Soliton wave solution of Eq.
$ (1.1) $ for$ \alpha=-0.3 $ ,$ \beta=-0.1 $ ,$ \gamma=-0.7 $ ,$ \kappa=0.5 $ ,$ b_{0}=0.5 $ , and$ b_{2}=-0.1 $ . -
Figure 3. Soliton rational solution of Eq.
$ (1.1) $ for$ \alpha=-0.075 $ ,$ \beta=-0.1 $ ,$ \gamma=0.3 $ ,$ \kappa=1 $ ,$ b_{0}=-1 $ ,$ b_{1}=0.5 $ ,$ q_{0}=0.4 $ and$ q_{1}=-1 $ . - Figure 4. Motion of single solitary wave and its contour
- Figure 5. Error norms for motion of the single solitary wave
- Figure 6. Interaction of two solitary waves and its contour
- Figure 7. Generated waves and its contour for Gaussian initial condition
- Figure 8. Generated waves and its contour for undular bore initial condition