On the semiclassical limit of the general modified NLS equation

Benoît Desjardins; Chi Kun Lin

doi:10.1006/jmaa.2001.7482

On the semiclassical limit of the general modified NLS equation

Benoît Desjardins^*
, Chi Kun Lin

^*Corresponding author for this work

Commissariat à l’énergie atomique et aux énergies alternatives
National Cheng Kung University

Research output: Contribution to journal › Article › peer-review

14 Citations (Scopus)

Abstract

We study the semiclassical limit of the so-called general modified nonlinear Schrödinger equation for initial data with Sobolev regularity, before shocks appear in the limit system. The strict hyperbolicity and genuine nonlinearity are proved for the dispersion limit of the cubic nonlinear case. The limiting transition from the MNLS equation to the NLS equation is also discussed.

Original language	English
Pages (from-to)	546-571
Number of pages	26
Journal	Journal of Mathematical Analysis and Applications
Volume	260
Issue number	2
DOIs	https://doi.org/10.1006/jmaa.2001.7482
Publication status	Published - 15 Aug 2001
Externally published	Yes

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10.1006/jmaa.2001.7482

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title = "On the semiclassical limit of the general modified NLS equation",

abstract = "We study the semiclassical limit of the so-called general modified nonlinear Schr{\"o}dinger equation for initial data with Sobolev regularity, before shocks appear in the limit system. The strict hyperbolicity and genuine nonlinearity are proved for the dispersion limit of the cubic nonlinear case. The limiting transition from the MNLS equation to the NLS equation is also discussed.",

author = "Beno{\^i}t Desjardins and Lin, \{Chi Kun\}",

note = "Funding Information: The authors thank Professors O. K. Pashaev and Jyh-Hao Lee for useful discussions. Chi-Kun Lin gratefully acknowledges the support from the National Science Council of Taiwan under Grant NSC 36195F. He thanks Professor Peter Markowich for his invitation and the Schr{\"o}dinger institute in Vienna, Austria, for their hospitality and support during his visits there.",

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AU - Desjardins, Benoît

AU - Lin, Chi Kun

N1 - Funding Information: The authors thank Professors O. K. Pashaev and Jyh-Hao Lee for useful discussions. Chi-Kun Lin gratefully acknowledges the support from the National Science Council of Taiwan under Grant NSC 36195F. He thanks Professor Peter Markowich for his invitation and the Schrödinger institute in Vienna, Austria, for their hospitality and support during his visits there.

PY - 2001/8/15

Y1 - 2001/8/15

N2 - We study the semiclassical limit of the so-called general modified nonlinear Schrödinger equation for initial data with Sobolev regularity, before shocks appear in the limit system. The strict hyperbolicity and genuine nonlinearity are proved for the dispersion limit of the cubic nonlinear case. The limiting transition from the MNLS equation to the NLS equation is also discussed.

AB - We study the semiclassical limit of the so-called general modified nonlinear Schrödinger equation for initial data with Sobolev regularity, before shocks appear in the limit system. The strict hyperbolicity and genuine nonlinearity are proved for the dispersion limit of the cubic nonlinear case. The limiting transition from the MNLS equation to the NLS equation is also discussed.

UR - https://www.scopus.com/pages/publications/0035882847

U2 - 10.1006/jmaa.2001.7482

DO - 10.1006/jmaa.2001.7482

M3 - Article

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EP - 571

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -

On the semiclassical limit of the general modified NLS equation

Abstract

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