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Lenells, Jonatanorcid.org/0000-0001-6191-7769

Open this publication in new window or tab >>Airy and Painleve asymptotics for the mKdV equation### Charlier, Christophe

### Lenells, Jonatan

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_0_j_idt188_some",{id:"formSmash:j_idt184:0:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_0_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_0_j_idt188_otherAuthors",{id:"formSmash:j_idt184:0:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_0_j_idt188_otherAuthors",multiple:true}); 2019 (English)In: Journal of the London Mathematical Society, ISSN 0024-6107, E-ISSN 1469-7750Article in journal (Refereed) Published
##### Abstract [en]

##### 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 ()
#####

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#####

##### Note

KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).

KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).

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.

QC 20190904

Available from: 2019-09-04 Created: 2019-09-04 Last updated: 2019-09-04Bibliographically approvedOpen this publication in new window or tab >>Exact Solution of a Neumann Boundary Value Problem for the Stationary Axisymmetric Einstein Equations### Lenells, Jonatan

### Pei, Long

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_1_j_idt188_some",{id:"formSmash:j_idt184:1:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_1_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_1_j_idt188_otherAuthors",{id:"formSmash:j_idt184:1:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_1_j_idt188_otherAuthors",multiple:true}); 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]

##### 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)
#####

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#####

##### Note

KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).

KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).

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.

QC 20190830

Available from: 2019-08-30 Created: 2019-08-30 Last updated: 2019-09-05Bibliographically approvedOpen this publication in new window or tab >>Long-time asymptotics for the Degasperis-Procesi equation on the half-line### De Monvel, Anne Boutet

### Lenells, Jonatan

### Shepelsky, Dmitry

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_2_j_idt188_some",{id:"formSmash:j_idt184:2:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_2_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_2_j_idt188_otherAuthors",{id:"formSmash:j_idt184:2:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_2_j_idt188_otherAuthors",multiple:true}); 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]

##### 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 ()
#####

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##### Note

Univ Paris Diderot, Inst Math Jussieu PRG, F-75205 Paris 13, France..

KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).

Inst Low Temp Phys, Math Div, UA-61103 Kharkov, Ukraine.;Kharkov Natl Univ, Sch Math & Comp Sci, UA-61022 Kharkov, Ukraine..

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.

QC 20190624

Available from: 2019-06-24 Created: 2019-06-24 Last updated: 2019-06-24Bibliographically approvedOpen this publication in new window or tab >>Schramm's Formula and the Green's Function for Multiple SLE### Lenells, Jonatan

### Viklund, Fredrik

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_3_j_idt188_some",{id:"formSmash:j_idt184:3:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_3_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_3_j_idt188_otherAuthors",{id:"formSmash:j_idt184:3:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_3_j_idt188_otherAuthors",multiple:true}); 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]

##### 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)
#####

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##### Note

KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.). KTH Royal Inst Technol, Dept Math, S-10044 Stockholm, Sweden..

KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).

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.

QC 20190924

Available from: 2019-09-24 Created: 2019-09-24 Last updated: 2019-09-24Bibliographically approvedOpen this publication in new window or tab >>Matrix Riemann-Hilbert problems with jumps across Carleson contours### Lenells, Jonatan

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_4_j_idt188_some",{id:"formSmash:j_idt184:4:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_4_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_4_j_idt188_otherAuthors",{id:"formSmash:j_idt184:4:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_4_j_idt188_otherAuthors",multiple:true}); 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]

##### 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)
#####

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##### Note

KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).

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.

QC 20180531

Available from: 2018-05-31 Created: 2018-05-31 Last updated: 2018-05-31Bibliographically approvedOpen this publication in new window or tab >>Nonlinear Fourier transforms for the sine-Gordon equation in the quarter plane### Huang, Lin

### Lenells, Jonatan

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_5_j_idt188_some",{id:"formSmash:j_idt184:5:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_5_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_5_j_idt188_otherAuthors",{id:"formSmash:j_idt184:5:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_5_j_idt188_otherAuthors",multiple:true}); 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]

##### 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)
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##### Funder

Swedish Research Council, 2015-05430
##### Note

KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).

KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).

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.

QC 20180223

Available from: 2018-02-23 Created: 2018-02-23 Last updated: 2018-06-19Bibliographically approvedOpen this publication in new window or tab >>The Nonlinear Steepest Descent Method for Riemann-Hilbert Problems of Low Regularity### Lenells, Jonatan

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_6_j_idt188_some",{id:"formSmash:j_idt184:6:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_6_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_6_j_idt188_otherAuthors",{id:"formSmash:j_idt184:6:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_6_j_idt188_otherAuthors",multiple:true}); 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]

##### 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)
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##### Funder

Swedish Research Council, 2015-05430EU, European Research Council, 682537
##### Note

KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).

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.

QC 20180111

Available from: 2018-01-11 Created: 2018-01-11 Last updated: 2018-01-11Bibliographically approvedOpen this publication in new window or tab >>Admissible boundary values for the defocusing nonlinear Schrödinger equation with asymptotically time-periodic data### Lenells, Jonatan

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_7_j_idt188_some",{id:"formSmash:j_idt184:7:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_7_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_7_j_idt188_otherAuthors",{id:"formSmash:j_idt184:7:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_7_j_idt188_otherAuthors",multiple:true}); 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]

##### 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)
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##### Note

KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).

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.

QC 20151210. QC 20160203

Available from: 2015-12-10 Created: 2015-10-09 Last updated: 2017-12-01Bibliographically approvedOpen this publication in new window or tab >>Nonlinear Fourier Transforms and the mKdV Equation in the Quarter Plane### Lenells, Jonatan

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_8_j_idt188_some",{id:"formSmash:j_idt184:8:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_8_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_8_j_idt188_otherAuthors",{id:"formSmash:j_idt184:8:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_8_j_idt188_otherAuthors",multiple:true}); 2015 (English)In: Studies in applied mathematics (Cambridge), ISSN 0022-2526, E-ISSN 1467-9590Article in journal (Refereed) Published
##### Abstract [en]

##### 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)
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##### Note

KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).

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.

QC 20151123

Available from: 2015-11-23 Created: 2015-11-02 Last updated: 2017-12-01Bibliographically approvedOpen this publication in new window or tab >>Optimal contracting under adverse selection: The implications of mentalizing### Lenells, Jonatan

### Stea, D.

### Foss, N.J.

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_9_j_idt188_some",{id:"formSmash:j_idt184:9:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_9_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_9_j_idt188_otherAuthors",{id:"formSmash:j_idt184:9:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_9_j_idt188_otherAuthors",multiple:true}); 2015 (English)In: Współczesna Ekonomia, ISSN 1897-9254, Vol. 9, no 2, p. 215-232Article in journal (Refereed) Published
##### Abstract [en]

##### National Category

Computer Sciences Information Systems, Social aspects
##### Identifiers

urn:nbn:se:kth:diva-174686 (URN)2-s2.0-84937439530 (Scopus ID)
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PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_9_j_idt188_j_idt371",{id:"formSmash:j_idt184:9:j_idt188:j_idt371",widgetVar:"widget_formSmash_j_idt184_9_j_idt188_j_idt371",multiple:true});
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##### Note

KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).

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.

QC 20151113

Available from: 2015-11-13 Created: 2015-10-07 Last updated: 2018-01-10Bibliographically approved