---
OA_type: closed access
_id: '22092'
abstract:
- lang: eng
  text: 'The first part of the book provides an introduction to key tools and techniques
    in dispersive equations: Strichartz estimates, bilinear estimates, modulation
    and adapted function spaces, with an application to the generalized Korteweg-de
    Vries equation and the Kadomtsev-Petviashvili equation. The energy-critical nonlinear
    Schrödinger equation, global solutions to the defocusing problem, and scattering
    are the focus of the second part. Using this concrete example, it walks the reader
    through the induction on energy technique, which has become the essential methodology
    for tackling large data critical problems. This includes refined/inverse Strichartz
    estimates, the existence and almost periodicity of minimal blow up solutions,
    and the development of long-time Strichartz inequalities. The third part describes
    wave and Schrödinger maps. Starting by building heuristics about multilinear estimates,
    it provides a detailed outline of this very active area of geometric/dispersive
    PDE. It focuses on concepts and ideas and should provide graduate students with
    a stepping stone to this exciting direction of research.​'
alternative_title:
- Oberwolfach Seminars
article_processing_charge: No
author:
- first_name: Herbert
  full_name: Koch, Herbert
  last_name: Koch
- first_name: Daniel
  full_name: Tataru, Daniel
  last_name: Tataru
- first_name: Monica
  full_name: Visan, Monica
  id: 056daca0-b8d1-11f0-964f-f91054abf8ca
  last_name: Visan
citation:
  ama: 'Koch H, Tataru D, Vişan M. <i>Dispersive Equations and Nonlinear Waves: Generalized
    Korteweg–de Vries, Nonlinear Schrödinger, Wave and Schrödinger Maps</i>. Vol 45.
    1st ed. Basel: Springer; 2014. doi:<a href="https://doi.org/10.1007/978-3-0348-0736-4">10.1007/978-3-0348-0736-4</a>'
  apa: 'Koch, H., Tataru, D., &#38; Vişan, M. (2014). <i>Dispersive Equations and
    Nonlinear Waves: Generalized Korteweg–de Vries, Nonlinear Schrödinger, Wave and
    Schrödinger Maps</i> (1st ed., Vol. 45). Basel: Springer. <a href="https://doi.org/10.1007/978-3-0348-0736-4">https://doi.org/10.1007/978-3-0348-0736-4</a>'
  chicago: 'Koch, Herbert, Daniel Tataru, and Monica Vişan. <i>Dispersive Equations
    and Nonlinear Waves: Generalized Korteweg–de Vries, Nonlinear Schrödinger, Wave
    and Schrödinger Maps</i>. 1st ed. Vol. 45. OWS. Basel: Springer, 2014. <a href="https://doi.org/10.1007/978-3-0348-0736-4">https://doi.org/10.1007/978-3-0348-0736-4</a>.'
  ieee: 'H. Koch, D. Tataru, and M. Vişan, <i>Dispersive Equations and Nonlinear Waves:
    Generalized Korteweg–de Vries, Nonlinear Schrödinger, Wave and Schrödinger Maps</i>,
    1st ed., vol. 45. Basel: Springer, 2014.'
  ista: 'Koch H, Tataru D, Vişan M. 2014. Dispersive Equations and Nonlinear Waves:
    Generalized Korteweg–de Vries, Nonlinear Schrödinger, Wave and Schrödinger Maps
    1st ed., Basel: Springer, 312p.'
  mla: 'Koch, Herbert, et al. <i>Dispersive Equations and Nonlinear Waves: Generalized
    Korteweg–de Vries, Nonlinear Schrödinger, Wave and Schrödinger Maps</i>. 1st ed.,
    vol. 45, Springer, 2014, doi:<a href="https://doi.org/10.1007/978-3-0348-0736-4">10.1007/978-3-0348-0736-4</a>.'
  short: 'H. Koch, D. Tataru, M. Vişan, Dispersive Equations and Nonlinear Waves:
    Generalized Korteweg–de Vries, Nonlinear Schrödinger, Wave and Schrödinger Maps,
    1st ed., Springer, Basel, 2014.'
date_created: 2026-06-19T08:54:09Z
date_published: 2014-07-31T00:00:00Z
date_updated: 2026-07-02T05:44:24Z
day: '31'
doi: 10.1007/978-3-0348-0736-4
edition: '1'
extern: '1'
intvolume: '        45'
language:
- iso: eng
month: '07'
oa_version: None
page: '312'
place: Basel
publication_identifier:
  eisbn:
  - '9783034807364'
  eissn:
  - 2296-5041
  isbn:
  - '9783034807357'
  issn:
  - 1661-237X
publication_status: published
publisher: Springer
quality_controlled: '1'
series_title: OWS
status: public
title: 'Dispersive Equations and Nonlinear Waves: Generalized Korteweg–de Vries, Nonlinear
  Schrödinger, Wave and Schrödinger Maps'
type: book
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 45
year: '2014'
...