Stability or instability of solitary waves to double dispersion equation with quadratic-cubic nonlinearity
| Autor: | Milena Dimova, N. Kutev, Natalia Kolkovska |
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| Rok vydání: | 2017 |
| Předmět: |
Physics
Numerical Analysis Conservation law General Computer Science Applied Mathematics Cubic nonlinearity 010102 general mathematics 0206 medical engineering Mathematical analysis Mathematics::Analysis of PDEs 02 engineering and technology 020601 biomedical engineering 01 natural sciences Stability (probability) Instability Theoretical Computer Science Nonlinear system Quadratic equation Modeling and Simulation Stability theory Dispersion relation 0101 mathematics |
| Zdroj: | Mathematics and Computers in Simulation. 133:249-264 |
| ISSN: | 0378-4754 |
| Popis: | The solitary waves to the double dispersion equation with quadratic-cubic nonlinearity are explicitly constructed. Grillakis, Shatah and Strauss’ stability theory is applied for the investigation of the orbital stability or instability of solitary waves to the double dispersion equation. An analytical formula, related to some conservation laws of the problem, is derived. As a consequence, the dependence of orbital stability or instability on the parameters of the problem is demonstrated. A complete characterization of the values of the wave velocity, for which the solitary waves to the generalized Boussinesq equation are orbitally stable or unstable, is given. In the special case of a quadratic nonlinearity our results are reduced to those known in the literature. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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