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

Details Explicit solutions to the Korteweg-de Vries equation on the half line Explicit solutions to the Korteweg-de Vries equation on the half line

2006-06-02

arxiv.org/abs/math-ph/0606008v2

Inverse Problems 22 (2006), 2165-2174

Physics

Mathematical Physics

17 pages, no figures

Scientific paper

10.1088/0266-5611/22/6/015

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.

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