Change search
Link to record
Permanent link

Direct link
BETA
Alternative names
Publications (10 of 72) Show all publications
Charlier, C. & Lenells, J. (2019). Airy and Painleve asymptotics for the mKdV equation. Journal of the London Mathematical Society
Open this publication in new window or tab >>Airy and Painleve asymptotics for the mKdV equation
2019 (English)In: Journal of the London Mathematical Society, ISSN 0024-6107, E-ISSN 1469-7750Article in journal (Refereed) Published
Abstract [en]

We consider the higher order asymptotics for the modified Korteweg-de Vries equation in the Painleve sector. We first show that the solution admits a uniform expansion to all orders in powers of t-1/3 with coefficients that are smooth functions of x(3t)-1/3. We then consider the special case when the reflection coefficient vanishes at the origin. In this case, the leading coefficient which satisfies the Painleve II equation vanishes. We show that the leading asymptotics are instead described by the derivative of the Airy function. We are also able to express the subleading term explicitly in terms of the Airy function.

Place, publisher, year, edition, pages
Wiley, 2019
Keywords
37K15, 41A60, 35Q15, 35Q53 (primary)
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-257450 (URN)10.1112/jlms.12265 (DOI)000480198900001 ()
Note

QC 20190904

Available from: 2019-09-04 Created: 2019-09-04 Last updated: 2019-09-04Bibliographically approved
Lenells, J. & Pei, L. (2019). Exact Solution of a Neumann Boundary Value Problem for the Stationary Axisymmetric Einstein Equations. Journal of nonlinear science, 29(4), 1621-1657
Open this publication in new window or tab >>Exact Solution of a Neumann Boundary Value Problem for the Stationary Axisymmetric Einstein Equations
2019 (English)In: Journal of nonlinear science, ISSN 0938-8974, E-ISSN 1432-1467, Vol. 29, no 4, p. 1621-1657Article in journal (Refereed) Published
Abstract [en]

For a stationary and axisymmetric spacetime, the vacuum Einstein field equations reduce to a single nonlinear PDE in two dimensions called the Ernst equation. By solving this equation with a Dirichlet boundary condition imposed along the disk, Neugebauer and Meinel in the 1990s famously derived an explicit expression for the spacetime metric corresponding to the Bardeen-Wagoner uniformly rotating disk of dust. In this paper, we consider a similar boundary value problem for a rotating disk in which a Neumann boundary condition is imposed along the disk instead of a Dirichlet condition. Using the integrable structure of the Ernst equation, we are able to reduce the problem to a Riemann-Hilbert problem on a genus one Riemann surface. By solving this Riemann-Hilbert problem in terms of theta functions, we obtain an explicit expression for the Ernst potential. Finally, a Riemann surface degeneration argument leads to an expression for the associated spacetime metric.

Place, publisher, year, edition, pages
Springer, 2019
Keywords
Ernst equation, Einstein equations, Boundary value problem, Unified transform method, Fokas method, Riemann-Hilbert problem, Theta function
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-257457 (URN)10.1007/s00332-018-9527-1 (DOI)000480743200011 ()2-s2.0-85059591310 (Scopus ID)
Note

QC 20190830

Available from: 2019-08-30 Created: 2019-08-30 Last updated: 2019-09-05Bibliographically approved
De Monvel, A. B., Lenells, J. & Shepelsky, D. (2019). Long-time asymptotics for the Degasperis-Procesi equation on the half-line. Annales de l'Institut Fourier, 69(1), 171-230
Open this publication in new window or tab >>Long-time asymptotics for the Degasperis-Procesi equation on the half-line
2019 (English)In: Annales de l'Institut Fourier, ISSN 0373-0956, E-ISSN 1777-5310, Vol. 69, no 1, p. 171-230Article in journal (Refereed) Published
Abstract [en]

We analyze the long-time asymptotics for the Degasperis- Procesi equation on the half-line. By applying nonlinear steepest descent techniques to an associated 3 x 3-matrix valued Riemann-Hilbert problem, we find an explicit formula for the leading order asymptotics of the solution in the similarity region in terms of the initial and boundary values.

Place, publisher, year, edition, pages
Annales de l'institut Fourier, 2019
Keywords
Degasperis-Procesi equation, long-time asymptotics, Riemann-Hilbert problem, boundary value problem
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-254126 (URN)000470077400005 ()
Note

QC 20190624

Available from: 2019-06-24 Created: 2019-06-24 Last updated: 2019-06-24Bibliographically approved
Lenells, J. & Viklund, F. (2019). Schramm's Formula and the Green's Function for Multiple SLE. Journal of statistical physics, 176(4), 873-931
Open this publication in new window or tab >>Schramm's Formula and the Green's Function for Multiple SLE
2019 (English)In: Journal of statistical physics, ISSN 0022-4715, E-ISSN 1572-9613, Vol. 176, no 4, p. 873-931Article in journal (Refereed) Published
Abstract [en]

We construct martingale observables for systems of multiple SLE curves by applying screening techniques within the CFT framework recently developed by Kang and Makarov, extended to admit multiple SLEs. We illustrate this approach by rigorously establishing explicit expressions for the Green's function and Schramm's formula in the case of two curves growing towards infinity. In the special case when the curves are "fused" and start at the same point, some of the formulas we prove were predicted in the physics literature.

Place, publisher, year, edition, pages
SPRINGER, 2019
Keywords
Integral asymptotics, Conformal field theory, Schramm-Loewner evolution
National Category
Telecommunications
Identifiers
urn:nbn:se:kth:diva-257558 (URN)10.1007/s10955-019-02325-0 (DOI)000479257200005 ()2-s2.0-85067080891 (Scopus ID)
Note

QC 20190924

Available from: 2019-09-24 Created: 2019-09-24 Last updated: 2019-09-24Bibliographically approved
Lenells, J. (2018). Matrix Riemann-Hilbert problems with jumps across Carleson contours. Monatshefte für Mathematik (Print), 186(1), 111-152
Open this publication in new window or tab >>Matrix Riemann-Hilbert problems with jumps across Carleson contours
2018 (English)In: Monatshefte für Mathematik (Print), ISSN 0026-9255, E-ISSN 1436-5081, Vol. 186, no 1, p. 111-152Article in journal (Refereed) Published
Abstract [en]

We develop a theory of n x n-matrix Riemann-Hilbert problems for a class of jump contours and jump matrices of low regularity. Our basic assumption is that the contour Gamma is a finite union of simple closed Carleson curves in the Riemann sphere. In particular, unbounded contours with cusps, corners, and nontransversal intersections are allowed. We introduce a notion of L-p-Riemann-Hilbert problem and establish basic uniqueness results and Fredholm properties. We also investigate the implications of Fredholmness for the unique solvability and prove a theorem on contour deformation.

Place, publisher, year, edition, pages
SPRINGER WIEN, 2018
Keywords
Matrix Riemann-Hilbert problem, Cauchy integral, Carleson contour
National Category
Algebra and Logic
Identifiers
urn:nbn:se:kth:diva-227214 (URN)10.1007/s00605-017-1019-0 (DOI)000430395800007 ()2-s2.0-85011002995 (Scopus ID)
Note

QC 20180531

Available from: 2018-05-31 Created: 2018-05-31 Last updated: 2018-05-31Bibliographically approved
Huang, L. & Lenells, J. (2018). Nonlinear Fourier transforms for the sine-Gordon equation in the quarter plane. Journal of Differential Equations, 264(5), 3445-3499
Open this publication in new window or tab >>Nonlinear Fourier transforms for the sine-Gordon equation in the quarter plane
2018 (English)In: Journal of Differential Equations, ISSN 0022-0396, E-ISSN 1090-2732, Vol. 264, no 5, p. 3445-3499Article in journal (Refereed) Published
Abstract [en]

Using the Unified Transform, also known as the Fokas method, the solution of the sine-Gordon equation in the quarter plane can be expressed in terms of the solution of a matrix Riemann-Hilbert problem whose definition involves four spectral functions a, b, A, B. The functions a(k) and b(k) are defined via a nonlinear Fourier transform of the initial data, whereas A(k) and B(k) are defined via a nonlinear Fourier transform of the boundary values. In this paper, we provide an extensive study of these nonlinear Fourier transforms and the associated eigenfunctions under weak regularity and decay assumptions on the initial and boundary values. The results can be used to determine the long-time asymptotics of the sine-Gordon quarter-plane solution via nonlinear steepest descent techniques.

Place, publisher, year, edition, pages
Academic Press, 2018
Keywords
Spectral function, Sine-Gordon equation, Inverse scattering, Initial-boundary value problem
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-223485 (URN)10.1016/j.jde.2017.11.023 (DOI)000424124500012 ()2-s2.0-85039794497 (Scopus ID)
Funder
Swedish Research Council, 2015-05430
Note

QC 20180223

Available from: 2018-02-23 Created: 2018-02-23 Last updated: 2018-06-19Bibliographically approved
Lenells, J. (2017). The Nonlinear Steepest Descent Method for Riemann-Hilbert Problems of Low Regularity. Indiana University Mathematics Journal, 66(4), 1287-1332
Open this publication in new window or tab >>The Nonlinear Steepest Descent Method for Riemann-Hilbert Problems of Low Regularity
2017 (English)In: Indiana University Mathematics Journal, ISSN 0022-2518, E-ISSN 1943-5258, Vol. 66, no 4, p. 1287-1332Article in journal (Refereed) Published
Abstract [en]

We prove a nonlinear steepest descent theorem for Riemann-Hilbert problems with Carleson jump contours and jump matrices of low regularity and slow decay. We illustrate the theorem by deriving the long-time asymptotics for the mKdV equation in the similarity sector for initial data with limited decay and regularity.

Place, publisher, year, edition, pages
Department of Mathematics, Indiana University, 2017
Keywords
Nonlinear steepest descent, Riemann-Hilbert problem, asymptotic analysis, long time asymptotics
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-221050 (URN)10.1512/iumj.2017.66.6078 (DOI)000418808700008 ()2-s2.0-85032286612 (Scopus ID)
Funder
Swedish Research Council, 2015-05430EU, European Research Council, 682537
Note

QC 20180111

Available from: 2018-01-11 Created: 2018-01-11 Last updated: 2018-01-11Bibliographically approved
Lenells, J. (2015). Admissible boundary values for the defocusing nonlinear Schrödinger equation with asymptotically time-periodic data. Journal of Differential Equations, 259(11), 5617-5639
Open this publication in new window or tab >>Admissible boundary values for the defocusing nonlinear Schrödinger equation with asymptotically time-periodic data
2015 (English)In: Journal of Differential Equations, ISSN 0022-0396, E-ISSN 1090-2732, Vol. 259, no 11, p. 5617-5639Article in journal (Refereed) Published
Abstract [en]

We consider solutions of the defocusing nonlinear Schrödinger equation in the quarter plane whose Dirichlet boundary data approach a single exponential αeiωt as t→∞. In order to determine the long time asymptotics of the solution, it is necessary to first characterize the asymptotic behavior of the Neumann value in terms of the given data. Assuming that the initial data decay as x→∞, we derive necessary conditions for the Neumann value to asymptote towards a single exponential of the form ceiωt. Since our approach yields expressions which relate α, ω, and c, the result can be viewed as a characterization of the large t behavior of the Dirichlet to Neumann map for single exponential profiles.

Place, publisher, year, edition, pages
Elsevier, 2015
Keywords
Initial-boundary value problem, Integrable system, Long-time asymptotics
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-175045 (URN)10.1016/j.jde.2015.07.003 (DOI)000367755900004 ()2-s2.0-84941806505 (Scopus ID)
Note

QC 20151210. QC 20160203

Available from: 2015-12-10 Created: 2015-10-09 Last updated: 2017-12-01Bibliographically approved
Lenells, J. (2015). Nonlinear Fourier Transforms and the mKdV Equation in the Quarter Plane. Studies in applied mathematics (Cambridge)
Open this publication in new window or tab >>Nonlinear Fourier Transforms and the mKdV Equation in the Quarter Plane
2015 (English)In: Studies in applied mathematics (Cambridge), ISSN 0022-2526, E-ISSN 1467-9590Article in journal (Refereed) Published
Abstract [en]

The unified transform method introduced by Fokas can be used to analyze initial-boundary value problems for integrable evolution equations. The method involves several steps, including the definition of spectral functions via nonlinear Fourier transforms and the formulation of a Riemann-Hilbert problem. We provide a rigorous implementation of these steps in the case of the mKdV equation in the quarter plane under limited regularity and decay assumptions. We give detailed estimates for the relevant nonlinear Fourier transforms. Using the theory of L2-RH problems, we consider the construction of quarter plane solutions which are C1 in time and C3 in space.

Place, publisher, year, edition, pages
Wiley-Blackwell, 2015
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-176204 (URN)10.1111/sapm.12089 (DOI)000368781700002 ()2-s2.0-84956832222 (Scopus ID)
Note

QC 20151123

Available from: 2015-11-23 Created: 2015-11-02 Last updated: 2017-12-01Bibliographically approved
Lenells, J., Stea, D. & Foss, N. (2015). Optimal contracting under adverse selection: The implications of mentalizing. Współczesna Ekonomia, 9(2), 215-232
Open this publication in new window or tab >>Optimal contracting under adverse selection: The implications of mentalizing
2015 (English)In: Współczesna Ekonomia, ISSN 1897-9254, Vol. 9, no 2, p. 215-232Article in journal (Refereed) Published
Abstract [en]

We study a model of adverse selection, hard and soft information, and mentalizing ability—the human capacity to represent others’ intentions, knowledge, and beliefs. By allowing for a continuous range of different information types, as well as for different means of acquiring information, we develop a model that captures how principals differentially obtain information on agents. We show that principals that combine conventional data collection techniques with mentalizing benefit from a synergistic effect that impacts both the amount of information that is accessed and the overall cost of that information. This strategy affects the properties of the optimal contract, which grows closer to the first best. This research provides insights into the implications of mentalizing for agency theory.

National Category
Computer Sciences Information Systems, Social aspects
Identifiers
urn:nbn:se:kth:diva-174686 (URN)2-s2.0-84937439530 (Scopus ID)
Note

QC 20151113

Available from: 2015-11-13 Created: 2015-10-07 Last updated: 2018-01-10Bibliographically approved
Organisations
Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0001-6191-7769

Search in DiVA

Show all publications