Properties of solutions (solitary wave) of systems of non linear dispersive equations
Higher order models for waves in nonlinear, dispersive media
| Full text | |
| Author(s): |
Pava, Jaime Angulo
Total Authors: 1
|
| Document type: | Journal article |
| Source: | Nonlinearity; v. 31, n. 3, p. 920-956, MAR 2018. |
| Web of Science Citations: | 2 |
| Abstract | |
This paper sheds new light on the stability properties of solitary wave solutions associated with Korteweg-de Vries-type models when the dispersion is very low. Using a compact, analytic approach and asymptotic perturbation theory, we establish sufficient conditions for the existence of exponentially growing solutions to the linearized problem and so a criterium of spectral instability of solitary waves is obtained for both models. Moreover, the nonlinear stability and spectral instability of the ground state solutions for both models is obtained for some specific regimen of parameters. Via a Lyapunov strategy and a variational analysis, we obtain the stability of the blow-up of solitary waves for the critical fractional KdV equation. The arguments presented in this investigation show promise for use in the study of the instability of traveling wave solutions of other nonlinear evolution equations. (AU) | |
| FAPESP's process: | 16/07311-0 - Schrodinger equations with point interactions and instability for the fractional Korteweg- de Vries equation |
| Grantee: | Jaime Angulo Pava |
| Support Opportunities: | Scholarships abroad - Research |