Submitting Campus
Daytona Beach
Department
Mathematics
Document Type
Article
Publication/Presentation Date
4-21-2022
Abstract/Description
When a (1 + 1)-dimensional nonlinear PDE in real function η(x, t) admits localized traveling solutions we can consider L to be the average width of the envelope, A the average value of the amplitude of the envelope, and V the group velocity of such a solution. The replacement rule (RR or nonlinear dispersion relation) procedure is able to provide a simple qualitative relation between these three parameters, without actually solve the equation. Examples are provided from KdV, C-H and BBM equations, but the procedure appears to be almost universally valid for such (1 + 1)-dimensional nonlinear PDE and their localized traveling solutions [3].
Publication Title
Nonlinear Sciences
Publisher
Cornell University
Scholarly Commons Citation
Ludu, A., & Zong, Z. (2022). The Replacement Rule for Nonlinear Shallow Water Waves. Nonlinear Sciences, (). Retrieved from https://commons.erau.edu/publication/2134
