Persistence of solutions to higher order nonlinear Schrödinger equation

Abstract

Applying an Abstract Interpolation Lemma, we showed persistence of solutions of the initial value problem to higher order nonlinear Schrödinger equation, also called Airy-Schrödinger equation, in weighted Sobolev spaces X 2,θ , for θ ∈ [0, 1].

Persistence property in weighted Sobolev spaces for nonlinear dispersive equations

“…

We generalize the Abstract Interpolation Lemma proved by the authors in [2]. Using this extension, we show in a more general context, the persistence property for the generalized Korteweg-de Vries equation, see (1.2), in the weighted Sobolev space with low regularity in the weight.

…”

“…In this section we generalize the Abstract Interpolation Lemma established by the authors in [2]. In fact, we extend in two directions: First, we generalize to multi-dimensional setting.…”

“…We are mainly concerned with the question of the persistence property in weighted Sobolev spaces for dispersive partial differential equations. Thus, the aim of this study is to generalize the Abstract Interpolation Lemma proved by the authors in [2], and to apply this new result to show, in a more general context, the persistence property of the initial-value problem for nonlinear dispersive equations. To be more precise, let us recall the persistence result we established in [2] for the Cauchy Problem for higher order nonlinear Schrödinger equation, that is…”

“…Our main focus in this paper is to show the persistence property, with respect to more general exponents, as explained below. To accomplish this, in the present paper we establish an extension of the abstract interpolation lemma proved in [2].…”

A remark on admissible triples for the generalized KdV equation

“…But if we consider solutions of (1.1) in weighted Sobolev spaces (see [17][18][19][20]) this norm is finite. In fact…”