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Selected Works of S.C. Mancas
Article
Stability of Solitary and Cnoidal Traveling Wave Solutions for a Fifth Order Korteweg-de Vries Equation
Applied Mathematics and Computation (2018)
  • Ronald Adams, Embry-Riddle Aeronautical University
  • S. C. Mancas, Embry-Riddle Aeronautical University
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Abstract
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.
Keywords
  • cnodial waves,
  • solitary waves,
  • fifth order KdV equation,
  • stability of traveling waves
Disciplines
Publication Date
March 15, 2018
DOI
https://doi.org/10.1016/j.amc.2017.11.005
Citation Information
Ronald Adams and S. C. Mancas. "Stability of Solitary and Cnoidal Traveling Wave Solutions for a Fifth Order Korteweg-de Vries Equation" Applied Mathematics and Computation Vol. 321 (2018) p. 745 - 751 ISSN: 0096-3003
Available at: http://works.bepress.com/stefani_mancas/77/