On the spectral stability of periodic traveling waves for the critical Korteweg-de Vries and Gardner equations
| Autor: | Fábio Natali, Sabrina Amaral, Eleomar Cardoso |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Vries equation
Physics Zero mean Partial differential equation Numerical analysis Mathematical analysis Spectral stability Galilean transformation symbols.namesake Nonlinear Sciences::Exactly Solvable and Integrable Systems Mathematics - Analysis of PDEs 76B25 35Q51 35Q53 symbols Traveling wave FOS: Mathematics Initial value problem Nonlinear Sciences::Pattern Formation and Solitons Analysis of PDEs (math.AP) |
| Popis: | In this paper, we determine spectral stability results of periodic waves for the critical Korteweg-de Vries and Gardner equations. For the first equation, we show that both positive and zero mean periodic traveling wave solutions possess a threshold value which may provides us a rupture in the spectral stability. Concerning the second equation, we establish the existence of periodic waves using a Galilean transformation on the periodic cnoidal solution for the modified Korteweg-de Vries equation and for both equations, the threshold values are the same. The main advantage presented in our paper concerns in solving some auxiliary initial value problems to obtain the spectral stability. 19 pages, 3 figures |
| Databáze: | OpenAIRE |
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