Skip to main content
SpringerLink
Log in
Book cover
  • Book
  • © 2019

Nonlinear PDEs, Their Geometry, and Applications

Proceedings of the Wisła 18 Summer School

Birkhäuser

Editors:

  1. Radosław A. Kycia

    1. The Faculty of Science, Masaryk University, Brno, Czech Republic

    View editor publications

    You can also search for this editor in PubMed   Google Scholar

  2. Maria Ułan

    1. Baltic Institute of Mathematics, Warszawa, Poland

    View editor publications

    You can also search for this editor in PubMed   Google Scholar

  3. Eivind Schneider

    1. Department of Mathematics and Statistics, UiT The Arctic University of Norway, Tromsø, Norway

    View editor publications

    You can also search for this editor in PubMed   Google Scholar

  • Collects talks given at the Summer School Wisla 18: Nonlinear PDEs, Their Geometry, and Applications in Wisla, Poland

  • Presents recent research the applications of nonlinear differential equations to physics

  • Provides a great starting point to understanding geometry theory of differential equations

Part of the book series: Tutorials, Schools, and Workshops in the Mathematical Sciences (TSWMS)

Sections

Buy it now

eBook USD 64.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 84.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

This is a preview of subscription content, access via your institution.

Table of contents (10 chapters)

  1. Front Matter

    Pages i-xvii
    PDF

  2. Lectures

    1. Front Matter

      Pages 1-1
      PDF

    2. Contact Geometry, Measurement, and Thermodynamics

      • Valentin V. Lychagin
      Pages 3-52

    3. Lectures on Geometry of Monge–Ampère Equations with Maple

      • Alexei Kushner, Valentin V. Lychagin, Jan Slovák
      Pages 53-94

    4. Geometry of Monge–Ampère Structures

      • Volodya Rubtsov
      Pages 95-156

  3. Participants Contributions

    1. Front Matter

      Pages 183-183
      PDF

    2. On the Geometry Arising in Some Meteorological Models in Two and Three Dimensions

      • Bertrand Banos, Volodya Roubtsov, Ian Roulstone
      Pages 185-207

    3. Gas Flow with Phase Transitions: Thermodynamics and the Navier–Stokes Equations

      • Anton A. Gorinov, Valentin V. Lychagin, Mikhail D. Roop, Sergey N. Tychkov
      Pages 209-222

    4. Differential Invariants in Thermodynamics

      • Eivind Schneider
      Pages 223-232

    5. Monge–Ampère Grassmannians, Characteristic Classes and All That

      • Valentin V. Lychagin, Volodya Roubtsov
      Pages 233-257

    7. Integrability of Geodesics of Totally Geodesic Metrics

      • Radosław A. Kycia, Maria Ułan
      Pages 267-275

  4. Back Matter

    Pages 277-279
    PDF
Back to top

About this book

This volume presents lectures given at the Summer School Wisła 18: Nonlinear PDEs, Their Geometry, and Applications, which took place from August 20 - 30th, 2018 in Wisła, Poland, and was organized by the Baltic Institute of Mathematics. The lectures in the first part of this volume were delivered by experts in nonlinear differential equations and their applications to physics. Original research articles from members of the school comprise the second part of this volume. Much of the latter half of the volume complements the methods expounded in the first half by illustrating additional applications of geometric theory of differential equations. Various subjects are covered, providing readers a glimpse of current research. Other topics covered include thermodynamics, meteorology, and the Monge–Ampère equations.


Researchers interested in the applications of nonlinear differential equations to physics will find this volume particularly useful. A knowledge of differential geometry is recommended for the first portion of the book, as well as a familiarity with basic concepts in physics.




Back to top

Keywords

  • Nonlinear Partial Differential Equations
  • Probability theory
  • Gaussian distribution
  • Summer School Wisla
  • Monge-Ampere Equations
  • Contact geometry
  • Tensor invariants
  • Recursion operators
  • Navier-Stokes equations
  • Geometry of Nonlinear PDEs
  • Baltic Institute of Mathematics
  • Thermodynamics
  • Meterology
  • Maple mathematics
  • partial differential equations
Back to top

Editors and Affiliations

  • The Faculty of Science, Masaryk University, Brno, Czech Republic

    Radosław A. Kycia

  • Baltic Institute of Mathematics, Warszawa, Poland

    Maria Ułan

  • Department of Mathematics and Statistics, UiT The Arctic University of Norway, Tromsø, Norway

    Eivind Schneider

Back to top

Bibliographic Information

Back to top
Access via your institution

Buy it now

eBook USD 64.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 84.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

search

Navigation