.png){kind=icon}
.png){kind=icon}
Return
A novel higher-order dispersive extension of the generalized Hunter-Saxton model: Traveling-wave solutions, time-fractional impacts, and qualitative analysis
.png){kind=icon}
PRE
AI
A
S
E
DOI：10.1142/S0217984926501058.png)
.png){kind=icon}
Original request for help.png){kind=icon}
Share.png){kind=icon}
Save
Abstract
En 中文
This study introduces and analyzes a new higher-order extension of the generalized Hunter-Saxton equation, which will be known by the fourth-order dispersive Hunter-Saxton equation.Unlike the classical version, novel fourth-order dispersive extension allows traveling-wave frameworks, that aren't applicable before. Closed-form soliton solutions, including rational (kink-type) and periodic, are derived via the extended auxiliary equation method. Existence of these solutions is shown through free parameters. To quantitatively assess the effects of time-fractional, modified Riemann-Liouville, beta, and M-truncated derivatives are considered. The corresponding traveling-wave reductions are illustrated to track these effects. Finally, the reduced dynamical system is examined numerically, revealing a remarkable sensitivity to starting data and bounded transverse oscillations. Also, the stability analysis shows a non-isolated equilibrium that induces the oscillating between neutral divergence, oscillatory centered, and hyperbolic saddle system. These results illustrate how both fourth-order dispersion and fractional-time structures enrich the dynamics of Hunter-Saxton model.
Keywords:
Dispersive Hunter-Saxton equation
extended auxiliary equation method
soliton
fractional derivative
sensitivity
stability
Journal
IF:
2.2
Papers:
207
Citations:
6.6K
Organization
Cited Papers