Submitting Campus
Daytona Beach
Department
Mathematics
Document Type
Article
Publication/Presentation Date
3-15-2018
Abstract/Description
We establish the nonlinear stability of solitary waves (solitons) and periodic traveling wave solutions (cnoidal waves) for a Korteweg-de Vries (KdV) equation which includes a fifth order dispersive term. The traveling wave solutions which yield solitons for zero boundary conditions and wave-trains of cnoidal waves for nonzero boundary conditions are analyzed using stability theorems, which rely on the positivity properties of the Fourier transforms. We show that all families of solutions considered here are (orbitally) stable.
Publication Title
Applied Mathematics and Computation
DOI
https://doi.org/10.1016/j.amc.2017.11.005
Publisher
Elsevier
Scholarly Commons Citation
Adams, R., & Mancas, S. (2018). Stability of Solitary and Cnoidal Traveling Wave Solutions for a Fifth Order Korteweg-de Vries Equation. Applied Mathematics and Computation, 321(). https://doi.org/10.1016/j.amc.2017.11.005
