Explicit solutions to the Korteweg–de Vries equation on the half line

2006/06/30 by Tuncay Aktosun, T. Aktosun, Cornelis van der Mee +1 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #math-ph #math.MP #msc:35Q51 #msc:35Q53 #msc:37K15 #nlin.SI

paper · pdf · doi:10.1088/0266-5611/22/6/015

published as Inverse Problems 22 (2006), 2165-2174 · 17 pages, no figures

openalex publication_date 2006/10/20 · arxiv created 2007/02/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Certain explicit solutions to the Korteweg–de Vries equation in the first quadrant of the xt-plane are presented. Such solutions involve algebraic
\ncombinations of truly elementary functions, and their initial values correspond to rational reflection coefficients in the associated Schrodinger equation. In the reflectionless case such solutions reduce to pure 
\nN-soliton solutions. An
\nillustrative example is provided.
\n

Citations

• Interaction of "Solitons" in a Collisionless Plasma and the Recurrence of Initial States

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