Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 35 min ago
Peer-reviewedCC BYScientific Reports

Soliton solutions and dynamical bifurcation analysis of the Yajima-Oikawa equations

  • Hezha H. Abdulkareem1
  • Hajar F. Ismael1
  • Shams Forruque Ahmed2
  • Muhammed I. Syam3
  1. 1Department of Mathematics, Faculty of Science, University of Zakho
  2. 2School of Mathematical Sciences, Sunway University,Bandar Sunway
  3. 3Department of Mathematical Sciences, UAE University
Read full textPDFDOICite

Abstract

The Yajima–Oikawa equations describes the resonant interaction between ion sound waves and Langmuir waves in plasma. Despite its importance, the detailed dynamical behavior of this model has not been comprehensively explored. In this work, we present a unified analytical and dynamical framework that combines exact solution construction with qualitative and quantitative analysis. By employing traveling wave transformations together with the first integral method, a class of exact solutions in terms of Jacobi elliptic functions is derived. These solutions are systematically classified, according to bifurcation scenarios, into periodic, quasi-periodic, solitary, and kink-type wave structures. To investigate the global dynamics, an external periodic perturbation is introduced, transforming the system into a higher-dimensional dynamical model. This enables the study of transitions between regular and chaotic regimes. The presence of chaos is confirmed through phase portraits, Poincaré sections, time series analysis, and Lyapunov exponent calculations, while sensitivity to initial conditions is also examined. The results provide a deeper understanding of nonlinear wave interactions and reveal rich dynamical features of the classical Yajima–Oikawa equations. These findings are relevant for applications in plasma physics and related fields, where accurate prediction and control of wave dynamics are essential, including in plasma-based devices such as fusion systems and wave propagation technologies.

Related

  1. Bifurcation analysis, optical soliton solutions and chaotic pattern for the stochastic DWDM topology with spatio-temporal dispersion
    Lu Tang
    High Energy Density PhysicsPeer-reviewedLicence not stated5 citedStatistical & nonlinear physicsOpenAlex
  2. Dynamical analysis and closed-form soliton solutions for the doubly dispersive equation
    Muhammad Zafarullah Baber, Muhammad Waqas Yasin, Khadeeja Arif +3
    Royal Society Open SciencePeer-reviewedCC BY 4.0Full textStatistical & nonlinear physicsCrossref
  3. Elliptic soliton solutions of lattice eigenfunction equations of the KdV type
    Xing Li, Ying Shi, Da-jun Zhang +1
    arXivPreprintCC BY 4.0Full textStatistical & nonlinear physicsarXiv
  4. Higher-order semi-rational solutions of the (2+1)-dimensional nonlocal multi-component Yajima--Oikawa system
    Wenqiang Lu, Kelei Tian, Ying Xu +2
    arXivPreprintCC BY 4.0Full textStatistical & nonlinear physicsarXiv
  5. Bifurcation structure of soliton self-injection locking in microresonators
    S. Deshmukh, T. M. Schneider, A. Tikan
    arXivPreprintarXiv licenceFull textOptics & photonicsStatistical & nonlinear physicsarXiv

Cite

BibTeXRIS
BibTeX
@article{abdulkareem2026soliton,
  title = {{Soliton solutions and dynamical bifurcation analysis of the Yajima-Oikawa equations}},
  author = {Hezha H. Abdulkareem and Hajar F. Ismael and Shams Forruque Ahmed and Muhammed I. Syam},
  journal = {Scientific Reports},
  year = {2026},
  month = aug,
  doi = {10.1038/s41598-026-55853-7},
  url = {https://doi.org/10.1038/s41598-026-55853-7},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - Soliton solutions and dynamical bifurcation analysis of the Yajima-Oikawa equations
AU  - Hezha H. Abdulkareem
AU  - Hajar F. Ismael
AU  - Shams Forruque Ahmed
AU  - Muhammed I. Syam
PY  - 2026
DA  - 2026/08/01
JO  - Scientific Reports
DO  - 10.1038/s41598-026-55853-7
UR  - https://doi.org/10.1038/s41598-026-55853-7
AB  - The Yajima–Oikawa equations describes the resonant interaction between ion sound waves and Langmuir waves in plasma. Despite its importance, the detailed dynamical behavior of this model has not been comprehensively explored. In this work, we present a unified analytical and dynamical framework that combines exact solution construction with qualitative and quantitative analysis. By employing traveling wave transformations together with the first integral method, a class of exact solutions in terms of Jacobi elliptic functions is derived. These solutions are systematically classified, according to bifurcation scenarios, into periodic, quasi-periodic, solitary, and kink-type wave structures. To investigate the global dynamics, an external periodic perturbation is introduced, transforming the system into a higher-dimensional dynamical model. This enables the study of transitions between regular and chaotic regimes. The presence of chaos is confirmed through phase portraits, Poincaré sections, time series analysis, and Lyapunov exponent calculations, while sensitivity to initial conditions is also examined. The results provide a deeper understanding of nonlinear wave interactions and reveal rich dynamical features of the classical Yajima–Oikawa equations. These findings are relevant for applications in plasma physics and related fields, where accurate prediction and control of wave dynamics are essential, including in plasma-based devices such as fusion systems and wave propagation technologies.
SN  - 2045-2322
ER  -