Physical significance and periodic solutions of the high-order good Jaulent-Miodek model in fluid dynamics
Using Whitham modulation theory, this paper examined periodic solutions and the problem of discontinuous initial values for the higher-order good Jaulent-Miodek (JM) equation. The physical significance of the JM equations was discussed by considering the reduction of Euler's equation. Next, the...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2024-11-01
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| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20241530?viewType=HTML |
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| Summary: | Using Whitham modulation theory, this paper examined periodic solutions and the problem of discontinuous initial values for the higher-order good Jaulent-Miodek (JM) equation. The physical significance of the JM equations was discussed by considering the reduction of Euler's equation. Next, the zero- and one-phase periodic solutions of the JM equation, along with the associated Whitham equations, were derived. The analysis included the degeneration of the one-phase periodic solution and the genus-one Whitham equation by examining the limits of the modulus
m of the Jacobi elliptic functions. Additionally, analytical and graphical representations of rarefaction wave solutions and periodic wave patterns were provided, and a solution for discontinuous initial values in the JM equation was presented. The results of this study offer a theoretical foundation for analyzing discontinuous initial values in nonlinear dispersion equations. |
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| ISSN: | 2473-6988 |