A Parametric Resonance for the Nonlocal Hirota–Maccari Equation
The nonlocal Hirota–Maccari equation is considered when a parametric excitation is acting over the frequency of a generic mode. Using the well-known asymptotic perturbation (AP) method, two coupled equations for the amplitude and phase can be obtained. We discovered the existence of an infinite-peri...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-07-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/14/7/1444 |
| _version_ | 1797433076285964288 |
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| author | Attilio Maccari |
| author_facet | Attilio Maccari |
| author_sort | Attilio Maccari |
| collection | DOAJ |
| description | The nonlocal Hirota–Maccari equation is considered when a parametric excitation is acting over the frequency of a generic mode. Using the well-known asymptotic perturbation (AP) method, two coupled equations for the amplitude and phase can be obtained. We discovered the existence of an infinite-period bifurcation when the parametric force increases its value. Moreover, symmetry considerations suggest performing a global analysis of the two couples, in such a way that we find an energy-like function and corroborate and verify the existence of this infinite period bifurcation. |
| first_indexed | 2024-03-09T10:11:58Z |
| format | Article |
| id | doaj.art-e498896a853d4276a582ed028cf42613 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T10:11:58Z |
| publishDate | 2022-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-e498896a853d4276a582ed028cf426132023-12-01T22:44:56ZengMDPI AGSymmetry2073-89942022-07-01147144410.3390/sym14071444A Parametric Resonance for the Nonlocal Hirota–Maccari EquationAttilio Maccari0Department of Physics, Istituto Superiore Piazza Resistenza, Piazza della Resistenza 1, 00015 Monterotondo, RM, ItalyThe nonlocal Hirota–Maccari equation is considered when a parametric excitation is acting over the frequency of a generic mode. Using the well-known asymptotic perturbation (AP) method, two coupled equations for the amplitude and phase can be obtained. We discovered the existence of an infinite-period bifurcation when the parametric force increases its value. Moreover, symmetry considerations suggest performing a global analysis of the two couples, in such a way that we find an energy-like function and corroborate and verify the existence of this infinite period bifurcation.https://www.mdpi.com/2073-8994/14/7/1444Hirota–Maccari equationinfinite-period bifurcationglobal analysisparametric excitation |
| spellingShingle | Attilio Maccari A Parametric Resonance for the Nonlocal Hirota–Maccari Equation Symmetry Hirota–Maccari equation infinite-period bifurcation global analysis parametric excitation |
| title | A Parametric Resonance for the Nonlocal Hirota–Maccari Equation |
| title_full | A Parametric Resonance for the Nonlocal Hirota–Maccari Equation |
| title_fullStr | A Parametric Resonance for the Nonlocal Hirota–Maccari Equation |
| title_full_unstemmed | A Parametric Resonance for the Nonlocal Hirota–Maccari Equation |
| title_short | A Parametric Resonance for the Nonlocal Hirota–Maccari Equation |
| title_sort | parametric resonance for the nonlocal hirota maccari equation |
| topic | Hirota–Maccari equation infinite-period bifurcation global analysis parametric excitation |
| url | https://www.mdpi.com/2073-8994/14/7/1444 |
| work_keys_str_mv | AT attiliomaccari aparametricresonanceforthenonlocalhirotamaccariequation AT attiliomaccari parametricresonanceforthenonlocalhirotamaccariequation |