Fractional derivative method for describing solitons on the surface of deep water
| Autor: | V. P. Krainov, V. I. Avrutskiy, Artur Ishkhanyan |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Physics
Surface (mathematics) Mathematical analysis Statistical and Nonlinear Physics Wave equation Third derivative Fractional calculus Gravitation Waves and shallow water symbols.namesake Nonlinear Sciences::Exactly Solvable and Integrable Systems symbols Dispersion (water waves) Nonlinear Sciences::Pattern Formation and Solitons Nonlinear Schrödinger equation Mathematical Physics |
| Zdroj: | Theoretical and Mathematical Physics. 208:1201-1206 |
| ISSN: | 1573-9333 0040-5779 |
| Popis: | The fractional derivative method is used to take wave dispersion into account in the wave equation when describing the propagation of gravitational soliton waves on the surface of deep water. This approach is similar to that used to obtain the Korteweg–de Vries equation for solitons on the surface of shallow water, where the dispersion term in the wave equation is the third derivative of the velocity. It provides an alternative to the well-known approach of Zakharov and others based on the model of the nonlinear Schrodinger equation. The obtained nonlinear integral equation can be solved numerically. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|