dimensions_id
pub.1105598020
Claudio
Muñoz
Gustavo
Ponce
https://scigraph.springernature.com/explorer/license/
en
2019-04-01
2019-04-11T14:19
1-18
https://link.springer.com/10.1007%2Fs00220-018-3206-9
true
2019-04
research_article
Breathers and the Dynamics of Solutions in KdV Type Equations
In this paper our first aim is to identify a large class of non-linear functions f(·) for which the IVP for the generalized Korteweg–de Vries equation does not have breathers or “small” breathers solutions. Also, we prove that all uniformly in time L1∩ H1 bounded solutions to KdV and related “small” perturbations must converge to zero, as time goes to infinity, locally in an increasing-in-time region of space of order t1/2 around any compact set in space. This set is included in the linearly dominated dispersive region x≪ t. Moreover, we prove this result independently of the well-known supercritical character of KdV scattering. In particular, no standing breather-like nor solitary wave structures exists in this particular regime.
articles
doi
10.1007/s00220-018-3206-9
abab4d5104aad15e4e33af6fe518d60d39dad9ce8380441bc58aec3513c6bc8a
readcube_id
Pure Mathematics
Springer Nature - SN SciGraph project
University of California, Santa Barbara
Department of Mathematics, University of California-Santa Barbara, 93106, Santa Barbara, CA, USA
Mathematical Sciences
University of Chile
CNRS and Departamento de Ingeniería Matemática DIM-CMM UMI 2807-CNRS, Universidad de Chile, Santiago, Chile
Communications in Mathematical Physics
0010-3616
1432-0916