Explicit solutions to the Korteweg-de Vries equation on the half line
Abstract
Certain explicit solutions to the Korteweg-de Vries equation in the first quadrant of the xt-plane are presented. Such solutions involve algebraic combinations of truly elementary functions, and their initial values correspond to rational reflection coefficients in the associated Schr\"odinger equation. In the reflectionless case such solutions reduce to pure N-soliton solutions. An illustrative example is provided.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.