Dispersive Partial Differential Equations
Dispersiva partiella differentialekvationer

FMA345F, 7.5 credits

Valid from: Spring 2026
Decided by: /Jonas Johansson
Date of establishment: 2026-01-15

General Information

Division: Mathematics
Course type: Third-cycle course
Teaching language: English

Aim

On completion of the course, participants shall be able to: Explain the dispersion phenomenon for linear dispersive equations. Understand and discuss main features of the two prototypical nonlinear dispersive PDEs: the Korteweg-de Vries and nonlinear Schrödinger equation. Identify problems that can be solved by methods that are part of the course

Goals

Knowledge and Understanding

For a passing grade the doctoral student must

• Explain in depth the concepts, theorems and methods included in the course
• Understand and discuss main features of the Korteweg-de Vries and nonlinear Schrödinger equations.

Competences and Skills

For a passing grade the doctoral student must

• Identify problems that can be solved by methods that are part of the course
• Describe the solution to a mathematical problem within the course framework, in speech and writing, logically coherent and with adequate terminology

Judgement and Approach

For a passing grade the doctoral student must For a passing grade the student must be able to identify the applicability and limitation of the tools and concepts discussed in the course to related problems in partial differential equations.

Course Contents

The course is an introduction to the concepts and analytical tools of nonlinear dispersive equations. We focus on existence theory and the long-time behavior of solutions. Prototypical examples such as the Korteweg–de Vries equation and the nonlinear Schrödinger equation will be discussed. We begin with the linear theory and examine how the dispersion relation influences the time decay of solutions. Incorporating nonlinear effects, we then turn to existence results and the long-term dynamics of solutions.

Course Literature

Linares, F. & Ponce, G.: Introduktion till icke-linjära dispersive ekvationer. 2015. ISBN 9781493921805.

Instruction Details

Types of instruction: Lectures, seminars

Examination Details

Examination format: Seminars given by participants
Grading scale: Failed, pass
Examiner:

Admission Details

Assumed prior knowledge: The course participants are assumed to have basic knowledge in the theory of partial differential equations, Sobolev spaces, and Fourier transformation

Course Occasion Information

Contact and Other Information

Course coordinators: