Study of Fixed Points and Chaos in Wave Propagation for the Generalized Damped Forced Korteweg-de Vries Equation using Bifurcation Analysis
In this article, we consider the Generalized Damped Forced Korteweg-de Vries (GDFKdV) equation. The forcing term considered is of the form $F(U)=U(U-v_1)(U-v_2)$, where $v_1$ and $v_2$ are free parameters. We investigate the behaviour of fixed points evaluated for the corresponding dynamical system...
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Akif AKGUL
2023-12-01
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| Series: | Chaos Theory and Applications |
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| Online Access: | https://dergipark.org.tr/en/download/article-file/3234725 |
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| author | Shruti Tomar Naresh M. Chadha |
| author_facet | Shruti Tomar Naresh M. Chadha |
| author_sort | Shruti Tomar |
| collection | DOAJ |
| description | In this article, we consider the Generalized Damped Forced Korteweg-de Vries (GDFKdV) equation. The forcing term considered is of the form $F(U)=U(U-v_1)(U-v_2)$, where $v_1$ and $v_2$ are free parameters. We investigate the behaviour of fixed points evaluated for the corresponding dynamical system of our model problem. With respect to these fixed points, we investigate the effects of a few significant parameters involved in the model, namely, the free parameters $v_1$ and $v_2$, the nonlinear, dispersion and damping coefficients using the tools from bifurcation analysis. We also obtain the wave plots for the critical values of the nonlinear and dispersion coefficients for which the system becomes unstable and exhibit chaotic behaviour. We confirm the chaos in our dynamical system under various conditions with the help of Lyapunov exponents. |
| format | Article |
| id | doaj-art-c8d5f9144a914b978cf48eea1a58cb3e |
| institution | Kabale University |
| issn | 2687-4539 |
| language | English |
| publishDate | 2023-12-01 |
| publisher | Akif AKGUL |
| record_format | Article |
| series | Chaos Theory and Applications |
| spelling | doaj-art-c8d5f9144a914b978cf48eea1a58cb3e2025-01-23T18:15:39ZengAkif AKGULChaos Theory and Applications2687-45392023-12-015428629210.51537/chaos.13204301971Study of Fixed Points and Chaos in Wave Propagation for the Generalized Damped Forced Korteweg-de Vries Equation using Bifurcation AnalysisShruti Tomar0https://orcid.org/0000-0002-0745-2988Naresh M. Chadha1https://orcid.org/0000-0003-1199-6408DIT UniversityDIT University Dehradun UttarakhandIn this article, we consider the Generalized Damped Forced Korteweg-de Vries (GDFKdV) equation. The forcing term considered is of the form $F(U)=U(U-v_1)(U-v_2)$, where $v_1$ and $v_2$ are free parameters. We investigate the behaviour of fixed points evaluated for the corresponding dynamical system of our model problem. With respect to these fixed points, we investigate the effects of a few significant parameters involved in the model, namely, the free parameters $v_1$ and $v_2$, the nonlinear, dispersion and damping coefficients using the tools from bifurcation analysis. We also obtain the wave plots for the critical values of the nonlinear and dispersion coefficients for which the system becomes unstable and exhibit chaotic behaviour. We confirm the chaos in our dynamical system under various conditions with the help of Lyapunov exponents.https://dergipark.org.tr/en/download/article-file/3234725gdfkdv equationnonlinear dynamicschaoswave propagationlyapunov exponentphase portraits |
| spellingShingle | Shruti Tomar Naresh M. Chadha Study of Fixed Points and Chaos in Wave Propagation for the Generalized Damped Forced Korteweg-de Vries Equation using Bifurcation Analysis Chaos Theory and Applications gdfkdv equation nonlinear dynamics chaos wave propagation lyapunov exponent phase portraits |
| title | Study of Fixed Points and Chaos in Wave Propagation for the Generalized Damped Forced Korteweg-de Vries Equation using Bifurcation Analysis |
| title_full | Study of Fixed Points and Chaos in Wave Propagation for the Generalized Damped Forced Korteweg-de Vries Equation using Bifurcation Analysis |
| title_fullStr | Study of Fixed Points and Chaos in Wave Propagation for the Generalized Damped Forced Korteweg-de Vries Equation using Bifurcation Analysis |
| title_full_unstemmed | Study of Fixed Points and Chaos in Wave Propagation for the Generalized Damped Forced Korteweg-de Vries Equation using Bifurcation Analysis |
| title_short | Study of Fixed Points and Chaos in Wave Propagation for the Generalized Damped Forced Korteweg-de Vries Equation using Bifurcation Analysis |
| title_sort | study of fixed points and chaos in wave propagation for the generalized damped forced korteweg de vries equation using bifurcation analysis |
| topic | gdfkdv equation nonlinear dynamics chaos wave propagation lyapunov exponent phase portraits |
| url | https://dergipark.org.tr/en/download/article-file/3234725 |
| work_keys_str_mv | AT shrutitomar studyoffixedpointsandchaosinwavepropagationforthegeneralizeddampedforcedkortewegdevriesequationusingbifurcationanalysis AT nareshmchadha studyoffixedpointsandchaosinwavepropagationforthegeneralizeddampedforcedkortewegdevriesequationusingbifurcationanalysis |