zbMATH — the first resource for mathematics

Explicit multiple singular periodic solutions and singular soliton solutions to KdV equation. (English) Zbl 1373.35273
Summary: Based on some stationary periodic solutions and stationary soliton solutions, one studies the general solution for the relative Lax system, and a number of exact solutions to the Korteweg-de Vries (KdV) equation are first constructed by the known Darboux transformation, these solutions include double and triple singular periodic solutions as well as singular soliton solutions whose amplitude depend on some rational functions.
35Q53 KdV equations (Korteweg-de Vries equations)
35C08 Soliton solutions
35B10 Periodic solutions to PDEs
Full Text: Link