Remarks on Existence/Nonexistence of Analytic Solutions to Higher Order KdV Equations
| Autor: | Anna Karczewska, Piotr Rozmej |
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| Rok vydání: | 2019 |
| Předmět: |
010302 applied physics
Mathematics::Analysis of PDEs FOS: Physical sciences General Physics and Astronomy Perturbation (astronomy) Mathematical Physics (math-ph) 02 engineering and technology 021001 nanoscience & nanotechnology 01 natural sciences Third order Nonlinear Sciences::Exactly Solvable and Integrable Systems Nonlinear wave equation 0103 physical sciences Applied mathematics 0210 nano-technology Korteweg–de Vries equation Nonlinear Sciences::Pattern Formation and Solitons Mathematical Physics Mathematics |
| Zdroj: | Acta Physica Polonica A. 136:910-915 |
| ISSN: | 0587-4246 1898-794X |
| DOI: | 10.12693/aphyspola.136.910 |
| Popis: | In this note, we discuss the existence of analytic solutions to the nonlinear wave equations of the higher order than the ubiquitous Korteweg-de Vries (KdV) equation. First, we recall our recent results which show that the extended KdV equation (KdV2), that is, the equation obtained within second-order perturbation approach possesses three kinds of analytic solutions. These solutions have the same functional form as the corresponding KdV solutions. We show, however, that the most intriguing multi-soliton solutions, known for the KdV equation, do not exist for KdV2. Moreover, we show that for the equations obtained in the third order perturbation approach (and then in any higher order) analytic solutions in the forms known from KdV theory do not exist. 7 pages |
| Databáze: | OpenAIRE |
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