Primitive solutions of the Korteweg–de Vries equation
| Autor: | Sergey A. Dyachenko, Dmitry Zakharov, Patrik V. Nabelek, Vladimir E. Zakharov |
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| Rok vydání: | 2020 |
| Předmět: |
Vries equation
Integrable system media_common.quotation_subject Mathematical analysis Statistical and Nonlinear Physics Function (mathematics) Interval (mathematics) Infinity 01 natural sciences Nonlinear Sciences::Exactly Solvable and Integrable Systems 0103 physical sciences 010307 mathematical physics Reflection coefficient 010306 general physics Korteweg–de Vries equation Nonlinear Sciences::Pattern Formation and Solitons Complex plane Mathematical Physics Mathematics media_common |
| Zdroj: | Theoretical and Mathematical Physics. 202:334-343 |
| ISSN: | 1573-9333 0040-5779 |
| DOI: | 10.1134/s0040577920030058 |
| Popis: | We survey recent results connected with constructing a new family of solutions of the Korteweg-de Vries equation, which we call primitive solutions. These solutions are constructed as limits of rapidly vanishing solutions of the Korteweg-de Vries equation as the number of solitons tends to infinity. A primitive solution is determined nonuniquely by a pair of positive functions on an interval on the imaginary axis and a function on the real axis determining the reflection coefficient. We show that elliptic one-gap solutions and, more generally, periodic finite-gap solutions are special cases of reflectionless primitive solutions. |
| Databáze: | OpenAIRE |
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