We study the semiclassical limit of the (generalized) KdV equation, for initial data with Sobolev regularity, before the time of the gradient catastrophe of the limit conservation law. In particular, we show that in the semiclassical limit the solution of the KdV equation: i) converges in Hs to the solution of the Hopf equation, provided the initial data belongs to Hs, ii) admits an asymptotic expansion in powers of the semiclassical parameter, if the initial data belongs to the Schwartz class. The result is also generalized to KdV equations with higher order linearities

Masoero, D., Raimondo, A. (2013). Semiclassical Limit for Generalized KdV Equations Before the Gradient Catastrophe. LETTERS IN MATHEMATICAL PHYSICS, 103, 559-583 [10.1007/s11005-013-0605-x].

Semiclassical Limit for Generalized KdV Equations Before the Gradient Catastrophe

RAIMONDO, ANDREA
Ultimo
2013

Abstract

We study the semiclassical limit of the (generalized) KdV equation, for initial data with Sobolev regularity, before the time of the gradient catastrophe of the limit conservation law. In particular, we show that in the semiclassical limit the solution of the KdV equation: i) converges in Hs to the solution of the Hopf equation, provided the initial data belongs to Hs, ii) admits an asymptotic expansion in powers of the semiclassical parameter, if the initial data belongs to the Schwartz class. The result is also generalized to KdV equations with higher order linearities
Articolo in rivista - Articolo scientifico
Semiclassical limit, KdV equation
English
559
583
25
Masoero, D., Raimondo, A. (2013). Semiclassical Limit for Generalized KdV Equations Before the Gradient Catastrophe. LETTERS IN MATHEMATICAL PHYSICS, 103, 559-583 [10.1007/s11005-013-0605-x].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/62618
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