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- Title
SOME LOCAL WELL POSEDNESS RESULTS IN WEIGHTED SOBOLEV SPACE H<sup>1/3</sup> FOR THE 3-KDV EQUATION.
- Authors
Castro, A. J.; Zhapsarbayeva, L. K.
- Abstract
The paper analyses the local well posedness of the initial value problem for the k-generalized Korteweg-de Vries equation for k = 3 with irregular initial data. k-generalized Korteweg-de Vries equations serve as a model of magnetoacoustic waves in plasma physics, of the nonlinear propagation of pulses in optical fibers. The solvability of many dispersive nonlinear equations has been studied in weighted Sobolev spaces in order to manage the decay at infinity of the solutions. We aim to extend these researches to the k-generalized KdV with k = 3. For initial data in classical Sobolev spaces there are many results in the literature for several nonlinear partial differential equations. However, our main interest is to investigate the situation for initial data in Sobolev weighted spaces, which is less understood. The low regularity Sobolev results for initial value problems for this dispersive equation was established in unweighted Sobolev spaces with s ≥ 1/12 and later further improved for s ≥ -1/6. The paper improves these results for 3-KdV equation with initial data from weighted Sobolev spaces.
- Subjects
SOBOLEV spaces; PLASMA physics; DUOPLASMATRONS; NONLINEAR equations; OPTICAL fibers
- Publication
Journal of Mathematics, Mechanics & Computer Science, 2023, Vol 120, Issue 4, p3
- ISSN
1563-0277
- Publication type
Article
- DOI
10.26577/JMMCS2023v120i4a1