Discussion Overview
The discussion revolves around the derivation of the 2D Korteweg-de Vries (KdV) equation, also referred to as the Kadomtsev-Petviashvili (KP) equation. Participants explore challenges related to weakly nonlinear theory and the extension of the derivation to include additional factors such as surface tension and electrical fields.
Discussion Character
- Exploratory, Technical explanation, Debate/contested
Main Points Raised
- One participant seeks references or derivations for the 2D KdV equation, indicating they have completed the linear theory but face challenges in the weakly nonlinear stage.
- Another participant references a paper by Johnson from 1980, suggesting it may contain relevant information for the derivation.
- A participant expresses intent to extend the derivation to include surface tension and electrical fields, noting prior success in one dimension but challenges in two dimensions.
- One participant mentions a footnote in a book by Drazin and Johnson that references the KdV equations, indicating that while the book discusses 2D solutions, it does not provide derivations.
- A participant finds the referenced paper helpful in addressing their derivation challenges and notes that the linear problem for the 3D case was not significantly more difficult than the 2D case, although plotting solutions proved to be time-consuming.
Areas of Agreement / Disagreement
Participants do not appear to reach a consensus on the derivation process or the inclusion of additional factors, indicating that multiple competing views and unresolved challenges remain in the discussion.
Contextual Notes
Limitations include the lack of detailed derivations in referenced materials and the potential dependence on specific assumptions regarding the effects of surface tension and electrical fields in the derivation process.