The Painleve Test and Reducibility to the Canonical Forms for Higher-Dimensional Soliton Equations with Variable-Coefficients
Abstract
The general KdV equation (gKdV) derived by T. Chou is one of the famous (1+1) dimensional soliton equations with variable coefficients. It is well-known that the gKdV equation is integrable. In this paper a higher-dimensional gKdV equation, which is integrable in the sense of the Painleve test, is presented. A transformation that links this equation to the canonical form of the Calogero-Bogoyavlenskii-Schiff equation is found. Furthermore, the form and similar transformation for the higher-dimensional modified gKdV equation are also obtained.
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.