Year: 2015
Type: article
Abstract: We study the initial value problem of the Korteweg–de Vries (KdV) equation on a space of generalized formal power series. We derive an explicit expression of the solution of the KdV equation with an arbitrary initial condition, using a recursively defined sequence of rational functions. From this result one can explain the formal analogues of the direct and inverse scattering transforms, relating the given initial condition to the solution of the formal Gelfand–Levitan–Marchenko equation.
Author: Namhoon Kim
Institution: Hongik University
Language: English
Topic: Nonlinear Waves and Solitons
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W2075418041