Numerical Solutions of Variable-Coefficient Fractional-in-Space KdV Equation with the Caputo Fractional Derivative
In this paper, numerical solutions of the variable-coefficient Korteweg-De Vries (vcKdV) equation with space described by the Caputo fractional derivative operator is developed. The propagation and interaction of vcKdV equation in different cases, such as breather soliton and periodic suppression so...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-04-01
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| Series: | Fractal and Fractional |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2504-3110/6/4/207 |
| _version_ | 1797504805299552256 |
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| author | Che Han Yu-Lan Wang |
| author_facet | Che Han Yu-Lan Wang |
| author_sort | Che Han |
| collection | DOAJ |
| description | In this paper, numerical solutions of the variable-coefficient Korteweg-De Vries (vcKdV) equation with space described by the Caputo fractional derivative operator is developed. The propagation and interaction of vcKdV equation in different cases, such as breather soliton and periodic suppression soliton, are numerically simulated. Especially, the Fourier spectral method is used to solve the fractional-in-space vcKdV equation with breather soliton. From numerical simulations and compared with other methods, it can be easily seen that our method has low computational complexity and higher precision. |
| first_indexed | 2024-03-10T04:09:35Z |
| format | Article |
| id | doaj.art-cdbedbcc3a4f43f09f6cff6ce1d5c048 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-10T04:09:35Z |
| publishDate | 2022-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-cdbedbcc3a4f43f09f6cff6ce1d5c0482023-11-23T08:15:32ZengMDPI AGFractal and Fractional2504-31102022-04-016420710.3390/fractalfract6040207Numerical Solutions of Variable-Coefficient Fractional-in-Space KdV Equation with the Caputo Fractional DerivativeChe Han0Yu-Lan Wang1Department of Mathematics, Inner Mongolia University of Technology, Hohhot 010051, ChinaDepartment of Mathematics, Inner Mongolia University of Technology, Hohhot 010051, ChinaIn this paper, numerical solutions of the variable-coefficient Korteweg-De Vries (vcKdV) equation with space described by the Caputo fractional derivative operator is developed. The propagation and interaction of vcKdV equation in different cases, such as breather soliton and periodic suppression soliton, are numerically simulated. Especially, the Fourier spectral method is used to solve the fractional-in-space vcKdV equation with breather soliton. From numerical simulations and compared with other methods, it can be easily seen that our method has low computational complexity and higher precision.https://www.mdpi.com/2504-3110/6/4/207fractional-in-space different equationvariable-coefficient KdV equationnumerical simulationsFourier spectral method |
| spellingShingle | Che Han Yu-Lan Wang Numerical Solutions of Variable-Coefficient Fractional-in-Space KdV Equation with the Caputo Fractional Derivative Fractal and Fractional fractional-in-space different equation variable-coefficient KdV equation numerical simulations Fourier spectral method |
| title | Numerical Solutions of Variable-Coefficient Fractional-in-Space KdV Equation with the Caputo Fractional Derivative |
| title_full | Numerical Solutions of Variable-Coefficient Fractional-in-Space KdV Equation with the Caputo Fractional Derivative |
| title_fullStr | Numerical Solutions of Variable-Coefficient Fractional-in-Space KdV Equation with the Caputo Fractional Derivative |
| title_full_unstemmed | Numerical Solutions of Variable-Coefficient Fractional-in-Space KdV Equation with the Caputo Fractional Derivative |
| title_short | Numerical Solutions of Variable-Coefficient Fractional-in-Space KdV Equation with the Caputo Fractional Derivative |
| title_sort | numerical solutions of variable coefficient fractional in space kdv equation with the caputo fractional derivative |
| topic | fractional-in-space different equation variable-coefficient KdV equation numerical simulations Fourier spectral method |
| url | https://www.mdpi.com/2504-3110/6/4/207 |
| work_keys_str_mv | AT chehan numericalsolutionsofvariablecoefficientfractionalinspacekdvequationwiththecaputofractionalderivative AT yulanwang numericalsolutionsofvariablecoefficientfractionalinspacekdvequationwiththecaputofractionalderivative |