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Dynamics and Exact Solitary Wave Structures of a Generalized Cubic--Quintic Fourth-Order AKNS Water-Wave Equation | ||
| Caspian Journal of Mathematical Sciences | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 21 آبان 1405 | ||
| نوع مقاله: Research Articles | ||
| شناسه دیجیتال (DOI): 10.22080/cjms.2026.32343.1888 | ||
| نویسنده | ||
| sarita pippal* | ||
| Department of Mathematics Punjab University Chandigarh sector 14 | ||
| تاریخ دریافت: 15 تیر 1405، تاریخ بازنگری: 31 شهریور 1405، تاریخ پذیرش: 06 آبان 1405 | ||
| چکیده | ||
| In this manuscript studied a generalised cubic--quintic fourth-order AKNS water-wave equation by extending the classical fourth-order AKNS equation by incorporating cubic--quintic nonlinear terms which provide a richer description of nonlinear wave phenomena. Exact travelling-wave solutions are constructed using the trial equation method (TEM)together with the generalized Riccati and logistic auxiliary equations, yields several new classes of exact analytical solutions. Furthermore, the equilibrium structure and local stability of the reduced travelling-wave system are investigated through Jacobian and eigenvalue analyses, and the analytical results are verified numerically by phase portraits. The inclusion of an external periodic forcing term transforms the reduced system into a three-dimensional autonomous dynamical system, enabling the investigation of periodic and chaotic travelling-wave dynamics. The obtained results demonstrate that the proposed generalized model possesses rich mathematical structures and supports diverse nonlinear wave patterns, providing new insights into higher-order nonlinear wave propagation. | ||
| کلیدواژه‌ها | ||
| Trial equation method؛ Exact travelling-wave solutions؛ Stability analysis؛ Chaotic dynamics؛ Nonlinear wave propagation | ||
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