Wave breaking conditions for a generalized Degasperis–Procesi equation
Abstract
A nonlinear equation encompassing the renowned Degasperis–Procesi model is investigated. The L2 conservation law of the nonlinear equation is derived, which has not been obtained in the previous literature and provides a foundational property for the equation. Utilizing the transport equation, the boundedness of the solutions is established. Finally, constructing Lyapunov functions, we derive the wave breaking criteria of the nonlinear equation both on the line and circle, depending on specific constraints imposed on the coefficients of the equation.
Fields of Study & Subjects
Nonlinear Waves and Solitons
Advanced Mathematical Physics Problems
Nonlinear Partial Differential Equations
Publication details
- Journal / source
- Applicable Analysis
- Volume
- 105
- Issue
- 14
- Pages
- 3125–3143
- Publication date
- 26 February 2026
- Language
- EN