Numerical Computation of Smooth and Peaked Decaying Traveling-Wave Solutions of the Degasperis–Procesi Equation: A Benchmark Study
4 affiliations
- 1Department of Natural Sciences, Southern University at New Orleans, 6801 Press Drive, New Orleans, LA 70126, USA
- 2Department of Mathematics & Information Technology, Concordia University of Edmonton, 7128 Ada Boulevard, Edmonton, AB T5B 4E4, Canada
- 3Department of Computer Science, Varna Free University, 9007 Varna, Bulgaria
- 4Rescale, 981 Mission Street, Unit #21, San Francisco, CA 94103, USA
Abstract
This work develops and benchmarks a numerical framework for computing decaying traveling-wave solutions of the Degasperis–Procesi equation. The approach provides a unified treatment of smooth solitary waves and peaked wave solutions across the relevant parameter regimes. Cusped and anticusped profiles are excluded, as their stronger singular behavior is not compatible with the regularity assumptions underlying the numerical formulation. The method addresses the challenges associated with the asymptotic behavior of the solutions and the non-smoothness of peaked profiles. Its performance is systematically assessed through convergence studies and comparisons with exact solutions. For smooth traveling waves, the numerical results exhibit the expected second-order convergence, while the computations for peaked waves demonstrate the method’s ability to resolve the non-smooth profile. The results also illustrate the dependence of wave profiles and amplitudes on wave speed and other model parameters, providing a benchmark for numerical computation of these solutions.
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BibTeX
@article{marinov2026numerical,
title = {{Numerical Computation of Smooth and Peaked Decaying Traveling-Wave Solutions of the Degasperis–Procesi Equation: A Benchmark Study}},
author = {Tchavdar T. Marinov and Rossitza S. Marinova and Radoslav Marinov},
journal = {Mathematics},
year = {2026},
month = nov,
doi = {10.3390/math14224171},
url = {https://www.mdpi.com/2227-7390/14/22/4171},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Numerical Computation of Smooth and Peaked Decaying Traveling-Wave Solutions of the Degasperis–Procesi Equation: A Benchmark Study
AU - Tchavdar T. Marinov
AU - Rossitza S. Marinova
AU - Radoslav Marinov
PY - 2026
DA - 2026/11/13
JO - Mathematics
DO - 10.3390/math14224171
UR - https://www.mdpi.com/2227-7390/14/22/4171
AB - This work develops and benchmarks a numerical framework for computing decaying traveling-wave solutions of the Degasperis–Procesi equation. The approach provides a unified treatment of smooth solitary waves and peaked wave solutions across the relevant parameter regimes. Cusped and anticusped profiles are excluded, as their stronger singular behavior is not compatible with the regularity assumptions underlying the numerical formulation. The method addresses the challenges associated with the asymptotic behavior of the solutions and the non-smoothness of peaked profiles. Its performance is systematically assessed through convergence studies and comparisons with exact solutions. For smooth traveling waves, the numerical results exhibit the expected second-order convergence, while the computations for peaked waves demonstrate the method’s ability to resolve the non-smooth profile. The results also illustrate the dependence of wave profiles and amplitudes on wave speed and other model parameters, providing a benchmark for numerical computation of these solutions.
SN - 2227-7390
ER -