Breathers and the Dynamics of Solutions in KdV Type Equations View Full Text


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Article Info

DATE

2019-04

AUTHORS

Claudio Muñoz, Gustavo Ponce

ABSTRACT

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. More... »

PAGES

1-18

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s00220-018-3206-9

DOI

http://dx.doi.org/10.1007/s00220-018-3206-9

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1105598020


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