## Abstract

This paper is concerned with regularizing effects of solutions to the (generalized) Korteweg-de Vries equation {∂_{t}u+∂_{x} ^{3}u=λu^{p−1}∂_{x}u,(t,x)∈ℝ×ℝ,u(0)=ϕ,x∈ℝ, and nonlinear Schrödinger equations in one space dimension {i∂_{t}u+12∂_{x} ^{2}u=G(u,u¯),(t,x)∈ℝ×ℝ,u(0)=ψ,x∈ℝ, where p is an integer satisfying p ≥ 2, λ ∊ ℂ and G is a polynomial of (u,u¯). We prove that if the initial function ϕ is in a Gevrey class of order 3 defined in Section 1, then there exists a positive time T such that the solution of (gKdV) is analytic in space variable for t ∊ [−T, T]\{0}, and if the initial function ψ in a Gevrey class of order 2, then there exists a positive time T such that the solution of (NLS) is analytic in space variable for t ∊ [−T, T]\{0}.

Original language | English |
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Pages (from-to) | 673-725 |

Number of pages | 53 |

Journal | Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire |

Volume | 12 |

Issue number | 6 |

DOIs | |

Publication status | Published - 1995 Nov 1 |

Externally published | Yes |

## ASJC Scopus subject areas

- Analysis
- Mathematical Physics
- Applied Mathematics