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Boundary value problems for nonlinear integrable equations

Total Cost €


EC-Contrib. €






Project "BOPNIE" data sheet

The following table provides information about the project.


Organization address
postcode: 100 44

contact info
title: n.a.
name: n.a.
surname: n.a.
function: n.a.
email: n.a.
telephone: n.a.
fax: n.a.

 Coordinator Country Sweden [SE]
 Total cost 2˙000˙000 €
 EC max contribution 2˙000˙000 € (100%)
 Programme 1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
 Code Call ERC-2015-CoG
 Funding Scheme ERC-COG
 Starting year 2016
 Duration (year-month-day) from 2016-05-01   to  2021-04-30


Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 


 Project objective

The purpose of this project is to develop new methods for solving boundary value problems (BVPs) for nonlinear integrable partial differential equations (PDEs). Integrable PDEs can be analyzed by means of the Inverse Scattering Transform, whose introduction was one of the most important developments in the theory of nonlinear PDEs in the 20th century. Until the 1990s the inverse scattering methodology was pursued almost entirely for pure initial-value problems. However, in many laboratory and field situations, the solution is generated by what corresponds to the imposition of boundary conditions rather than initial conditions. Thus, an understanding of BVPs is crucial.

In an exciting sequence of events taking place in the last two decades, new tools have become available to deal with BVPs for integrable PDEs. Although some important issues have already been resolved, several major problems remain open. The aim of this project is to solve a number of these open problems and to find solutions of BVPs which were heretofore not solvable. More precisely, the proposal has eight objectives:

1. Develop methods for solving problems with time-periodic boundary conditions.

2. Answer some long-standing open questions raised by series of wave-tank experiments 35 years ago.

3. Develop a new approach for the study of space-periodic solutions.

4. Develop new approaches for the analysis of BVPs for equations with 3 x 3-matrix Lax pairs.

5. Derive new asymptotic formulas by using a nonlinear version of the steepest descent method.

6. Construct disk and disk/black-hole solutions of the stationary axisymmetric Einstein equations.

7. Solve a BVP in Einstein's theory of relativity describing two colliding gravitational waves. 8. Extend the above methods to BVPs in higher dimensions.


year authors and title journal last update
List of publications.
2017 Lenells, Jonatan; Viklund, Fredrik
Schramm\'s formula and the Green\'s function for multiple SLE
published pages: , ISSN: , DOI:
2018 Mauersberger, Julian
The hyperbolic Ernst--Maxwell equations in a triangular domain
published pages: , ISSN: , DOI:
2019 Jonatan Lenells, Long Pei
Exact Solution of a Neumann Boundary Value Problem for the Stationary Axisymmetric Einstein Equations
published pages: , ISSN: 0938-8974, DOI: 10.1007/s00332-018-9527-1
Journal of Nonlinear Science 2019-08-05
2019 Jerry L. Bona and Jonatan Lenells
The KdV equation on the half-line: Time-periodicity and mass transport
published pages: , ISSN: , DOI:
2019 Charlier, C.; Lenells, J.
Airy and Painlev\'e asymptotics for the mKdV equation
published pages: , ISSN: , DOI:
2019 Huang, Lin; Lenells, Jonatan
Asymptotics for the Sasa--Satsuma equation in terms of a modified Painlev\'e II transcendent
published pages: , ISSN: , DOI:
2018 Geyer, Anna; Quirchmayr, Ronald
Shallow water models for stratified equatorial flows
published pages: , ISSN: , DOI:
2019 Lenells, Jonatan; Quirchmayr, Ronald
\"On the spectral problem associated with the time-periodic nonlinear Schr\"\"odinger equation\"\"\"
published pages: , ISSN: , DOI:
2018 Lenells, Jonatan; Viklund, Fredrik
Asymptotic analysis of Dotsenko-Fateev integrals
published pages: , ISSN: , DOI:
2019 Charlier, Christophe; Gharakhloo, Roozbeh
Asymptotics of Hankel determinants with a Laguerre-type or Jacobi-type potential and Fisher-Hartwig singularities
published pages: , ISSN: , DOI:
2018 Lenells, Jonatan; Mauersberger, Julian
The hyperbolic Ernst equation in a triangular domain
published pages: , ISSN: , DOI:
2018 Ronald Quirchmayr
A steady, purely azimuthal flow model for the Antarctic Circumpolar Current
published pages: 565-572, ISSN: 0026-9255, DOI: 10.1007/s00605-017-1097-z
Monatshefte für Mathematik 187/3 2019-07-22
2019 Julian Mauersberger
Asymptotics to all orders of the Euler–Darboux equation in a triangle
published pages: 180-196, ISSN: 0022-247X, DOI: 10.1016/j.jmaa.2018.10.071
Journal of Mathematical Analysis and Applications 471/1-2 2019-07-22
2018 Lin Huang, Jonatan Lenells
Construction of solutions and asymptotics for the sine-Gordon equation in the quarter plane
published pages: , ISSN: 2058-5985, DOI: 10.1093/integr/xyy014
Journal of Integrable Systems 3/1 2019-07-22
2018 Lenells, Jonatan
Matrix Riemann–Hilbert problems with jumps across Carleson contours
published pages: , ISSN: 0026-9255, DOI: 10.13039/501100003426
Monatshefte für Mathematik 9 2019-07-22
2017 Anna Geyer, Ronald Quirchmayr
Shallow water equations for equatorial tsunami waves
published pages: 20170100, ISSN: 1364-503X, DOI: 10.1098/rsta.2017.0100
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 376/2111 2019-07-22
2017 Jonatan Lenells
The nonlinear steepest descent method for Riemann-Hilbert problems of low regularity
published pages: 1287-1332, ISSN: 0022-2518, DOI: 10.1512/iumj.2017.66.6078
Indiana University Mathematics Journal 66/4 2019-07-22
2017 Lynnyngs Kelly Arruda, Jonatan Lenells
Long-time asymptotics for the derivative nonlinear Schrödinger equation on the half-line
published pages: 4141-4172, ISSN: 0951-7715, DOI: 10.1088/1361-6544/aa84c6
Nonlinearity 30/11 2019-07-22
2017 Lin Huang, Jonatan Lenells
Nonlinear Fourier transforms for the sine-Gordon equation in the quarter plane
published pages: , ISSN: 0022-0396, DOI:
Journal of Differential Equations 2019-07-22
2016 Jonatan Lenells
Absence of Solitons for the Defocusing NLS Equation on the Half-line
published pages: 1235-1241, ISSN: 0377-9017, DOI: 10.1007/s11005-016-0867-1
Letters in Mathematical Physics 106/9 2019-07-22

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