Jean-Philippe Lessard

Publications

82 research articles, numbered as in my CV. Links to preprints and codes are given when available.

Preprints 2

  1. [82]
    Platonic constellations of periodic motions in the (n+1)- body problem Preprint
    K. Constantineau, C. García-Azpeitia and J.-P. Lessard
    Preprint, 2026
    arXiv:2609.10242
  2. [81]
    Rigorous Validation of Cusp Bifurcations of Stationary Periodic Patterns in Partial Differential Equations Preprint
    D. Blanco and J.-P. Lessard
    Preprint, 2026
    arXiv:2608.15613

Accepted for publication 3

  1. [80]
    Spatially inhomogeneous two-cycles in an integrodifference equation To appear
    K. Church, K. Constantineau and J.-P. Lessard
    To appear in SIAM Journal on Applied Dynamical Systems, 2026
    arXiv:2510.21134
  2. [79]
    From heteroclinic loops to homoclinic snaking in reversible systems: rigorous forcing through computer-assisted proofs To appear
    J.B. van den Berg, G. Duchesne and J.-P. Lessard
    To appear in SIAM Journal on Applied Dynamical Systems, 2026
    arXiv:2507.16798
  3. [78]
    From the Lagrange Triangle to the Figure Eight Choreography: Proof of Marchal’s Conjecture To appear
    R. Calleja, C. García-Azpeitia, O. Hénot, J.-P. Lessard and J.D. Mireles James
    To appear in the Transactions of the American Mathematical Society, 2026
    arXiv:2406.17564

Published 77

2026

  1. [77]
    Recent advances about the rigorous integration of parabolic PDEs via fully spectral Fourier-Chebyshev expansions
    M. Cadiot and J.-P. Lessard
    Numerische Mathematik, 158(4): 1237–1289, 2026
    arXiv:2502.20644
  2. [76]
    Computer-Assisted Proofs of Solitons in Bose-Einstein Condensates
    M. Ayala, C. García-Azpeitia and J.-P. Lessard
    Journal of Nonlinear Science, 36(2), Paper No. 28, 2026
    arXiv:2503.04701

2025

  1. [75]
    Periodic localized traveling waves in the two-dimensional suspension bridge equation
    L. van der Aalst, J.B. van den Berg and J.-P. Lessard
    Nonlinearity, 38(7), Paper No. 075029, 2025
    arXiv:2405.19759
  2. [74]
    Validated matrix multiplication transform for orthogonal polynomials with applications to computer-assisted proofs for PDEs
    M. Cadiot, J. Jaquette, J.-P. Lessard and A. Takayasu
    Communications in Nonlinear Science and Numerical Simulation, Volume 151, Paper No. 109063, 2025
    arXiv:2411.18361
  3. [73]
    Cusp bifurcations: numerical detection via two-parameter continuation and computer-assisted proofs of existence
    J.-P. Lessard and A. Pugliese
    Discrete and Continuous Dynamical Systems - Series B, 30(6): 2135–2158, 2025
    arXiv:2404.00535
  4. [72]
    Determination of stable branches of relative equilibria of the N-vortex problem on the sphere
    K. Constantineau, C. García-Azpeitia, L.C. García-Naranjo and J.-P. Lessard
    Communications in Mathematical Physics, 406(2), 47 pages, 2025
    arXiv:2309.04320
  5. [71]
    A rigorous integrator and global existence for higher-dimensional semilinear parabolic PDEs via semigroup theory
    G. Duchesne, J.-P. Lessard and A. Takayasu
    Journal of Scientific Computing, 102(3), Paper No. 62, 66 pages, 2025
    arXiv:2402.00406
  6. [70]
    Stationary non-radial localized patterns in the planar Swift-Hohenberg PDE: constructive proofs of existence
    M. Cadiot, J.-P. Lessard and J.-C. Nave
    Journal of Differential Equations, Volume 414, 555–608, 2025
    arXiv:2403.10450

2024

  1. [69]
    Rigorous computation of solutions of semi-linear PDEs on unbounded domains via spectral methods
    M. Cadiot, J.-P. Lessard and J.-C. Nave
    SIAM Journal on Applied Dynamical Systems, 23(3): 1966–2017, 2024
    arXiv:2302.12877
  2. [68]
    Towards computational Morse-Floer homology: forcing results for connecting orbits by computing relative indices of critical points
    J.B. van den Berg, M. Gameiro, J.-P. Lessard and R.C. Vandervorst
    Foundations of Computational Mathematics, 24(5): 1739–1776, 2024
    arXiv:2206.09205 Code

2023

  1. [67]
    Numerical computation of transverse homoclinic orbits for periodic solutions of delay differential equations
    O. Hénot, J.-P. Lessard and J.D. Mireles James
    SIAM Journal on Applied Dynamical Systems, 22(4): 3093–3129, 2023
    arXiv:2304.00318
  2. [66]
    Constructive proofs for localized radial solutions of semilinear elliptic systems on ℝd
    J.B. van den Berg, O. Hénot and J.-P. Lessard
    Nonlinearity, 36(12): 6476–6512, 2023
    arXiv:2211.16445
  3. [65]
    Worrisome properties of neural network controllers and their symbolic representations
    J. Cyranka, K. Church and J.-P. Lessard
    Proceedings of the 2023 European Conference on Artificial Intelligence (ECAI 2023), Volume 372, pages 517-525, 2023
    arXiv:2307.15456
  4. [64]
    Persistence of periodic orbits under state-dependent delayed perturbations: computer-assisted proofs
    J. Gimeno, J.-P. Lessard, J.D. Mireles James and J. Yang
    SIAM Journal on Applied Dynamical Systems, 22(3): 1743–1779, 2023
    arXiv:2111.06391
  5. [63]
    Saddle-type blow-up solutions with computer-assisted proofs: validation and extraction of global nature
    J.-P. Lessard, K. Matsue and A. Takayasu
    Journal of Nonlinear Science, 33(1), Paper No. 46, 2023
    arXiv:2103.12390
  6. [62]
    Periodic orbits in Hořava-Lifshitz cosmologies
    K. Church, O. Hénot, P. Lappicy, J.-P. Lessard and H. Sprink
    General Relativity and Gravitation, 55(1), Paper No. 2, 2023
    arXiv:2203.03763

2022

  1. [61]
    Rigorous numerics for nonlinear heat equations in the complex plane of time
    A. Takayasu, J.-P. Lessard, J. Jaquette and H. Okamoto
    Numerische Mathematik, 151(3), 693–750, 2022
    arXiv:1910.12472
  2. [60]
    Rotation invariant patterns for a nonlinear Laplace-Beltrami equation: a Taylor-Chebyshev series approach
    J.B. van den Berg, G. Duchesne and J.-P. Lessard
    Journal of Computational Dynamics, 9(2): 253–278, 2022
    PDF Code
  3. [59]
    Global dynamics in nonconservative nonlinear Schrödinger equations
    J. Jaquette, J.-P. Lessard and A. Takayasu
    Advances in Mathematics, Volume 398, Paper 108234, 2022
    arXiv:2012.09734
  4. [58]
    Microscopic patterns in the 2D phase-field-crystal model
    G. Martine La Boissonière, R. Choksi and J.-P. Lessard
    Nonlinearity, 35(3), 1500–1520, 2022
    arXiv:2102.02338
  5. [57]
    Validated forward integration scheme for parabolic PDEs via Chebyshev series
    J. Cyranka and J.-P. Lessard
    Communications in Nonlinear Science and Numerical Simulation, Volume 109, Paper No. 106304, 2022
    arXiv:2101.00684
  6. [56]
    Singularities and heteroclinic connections in complex-valued evolutionary equations with a quadratic nonlinearity
    J. Jaquette, J.-P. Lessard and A. Takayasu
    Communications in Nonlinear Science and Numerical Simulation, Volume 107, Paper No. 106188, 2022
    arXiv:2109.00159
  7. [55]
    Rigorous verification of Hopf bifurcations in functional differential equations
    K. Church and J.-P. Lessard
    Physica D, Volume 429, Paper No. 133072, 2022
    PDF Code
  8. [54]
    Spatial relative equilibria and periodic orbit of the Coulomb (n+1) body problem
    K. Constantineau, C. García-Azpeitia and J.-P. Lessard
    Qualitative Theory of Dynamical Systems, 21(3): 1–19, 2022
    arXiv:2107.05118
  9. [53]
    Parameterization of unstable manifolds for DDEs: formal series solutions and validated error bounds
    O. H{énot, J.-P. Lessard and J.D. Mireles James
    Journal of Dynamics and Differential Equations, 34(2): 1285–1324, 2022
    Code
  10. [52]
    A general method for computer-assisted proofs of periodic solutions in delay differential problems
    J.B. van den Berg, C. Groothedde and J.-P. Lessard
    Journal of Dynamics and Differential Equations, 34(2):853–896, 2022
    PDF Code

2021

  1. [51]
    Rigorous verification of Hopf bifurcations via desingularization and continuation
    J.B. van den Berg, J.-P. Lessard and E. Queirolo
    SIAM Journal on Applied Dynamical Systems, 20(2):573–607, 2021
    arXiv:2006.13373
  2. [50]
    Spontaneous periodic orbits in the Navier-Stokes flow
    J.B. van den Berg, M. Breden, J.-P. Lessard and L. van Veen
    Journal of Nonlinear Science, 31(2): paper No. 41 (61 pages), 2021
    arXiv:1902.00384
  3. [49]
    From the Lagrange polygon to the figure eight I: Numerical evidence extending a conjecture of Marchal
    R. Calleja, C. García-Azpeitia, J.-P. Lessard and J.D. Mireles James
    Celestial Mechanics and Dynamical Astronomy, 133 (10): 1–20, 2021
    arXiv:2012.10759
  4. [48]
    Torus knot choreographies in the n-body problem
    R. Calleja, C. García-Azpeitia, J.-P. Lessard and J.D. Mireles James
    Nonlinearity, 34 (1): 313–349, 2021
    arXiv:1901.03738
  5. [47]
    A rigorous implicit C1 Chebyshev integrator for delay equations
    J.-P. Lessard and J.D. Mireles James
    Journal of Dynamics and Differential Equations, 33(4): 1959–1988, 2021

2020

  1. [46]
    Free vibrations in a wave equation modeling MEMS
    C. García-Azpeitia and J.-P. Lessard
    SIAM Journal on Applied Dynamical Systems, 19 (4): 2749–2782, 2020
    arXiv:2003.01365
  2. [45]
    A functional analytic approach to validated numerics for eigenvalues of delay equations
    J.-P. Lessard and J.D. Mireles James
    Journal of Computational Dynamics, 7(1): 123–158, 2020
    PDF Code
  3. [44]
    Traveling wave oscillatory patterns in a signed Kuramoto-Sivashinsky equation with absorption
    Y. Alama and J.-P. Lessard
    Journal of Computational and Applied Mathematics, 372 (112608), 2020
    PDF arXiv:1812.01166 Code

2019

  1. [43]
    Spatial periodic orbits in the equilateral circular restricted four body problem: computer assisted proofs of existence
    J. Burgos-Garcia, J.-P. Lessard and J.D. Mireles James
    Celestial Mechanics and Dynamical Astronomy, 131(1): 1–36, 2019

2018

  1. [42]
    Computer-assisted proofs for radially symmetric solutions of PDEs
    I. Balazs, J.B. van den Berg, J. Courtois, J. Dudas, J.-P. Lessard, A. Vörös- Kiss, JF Williams and X.Y. Yin
    Journal of Computational Dynamics, 5(1-2): 61–80, 2018
    PDF
  2. [41]
    Continuation of solutions and studying delay differential equations via rigorous numerics
    J.-P. Lessard
    Rigorous numerics in dynamics, 81–122, Proc. Sympos. Appl. Math., 74, Amer. Math. Soc., Providence, RI, 2018
    PDF Code
  3. [40]
    Parameterization of invariant manifolds for periodic orbits (II): a-posteriori analysis and computer assisted error bounds
    R. Castelli, J.-P. Lessard and J.D. Mireles James
    Journal of Dynamics and Differential Equations, 30(4): 1525–1581, 2018
    PDF
  4. [39]
    Computing discrete convolutions with verified accuracy via Banach algebras and the FFT
    J.-P. Lessard
    Applications of Mathematics, 63(3), 219–235, 2018
    PDF
  5. [38]
    Polynomial interpolation and a priori bootstrap for computer-assisted proofs in nonlinear ODEs
    M. Breden and J.-P. Lessard
    Discrete and Continuous Dynamical Systems - Series B, 23(7):2825–2858, 2018
    PDF arXiv:1704.03128 Code
  6. [37]
    Rigorous numerics for ill-posed PDEs: periodic orbits in the Boussinesq equation
    R. Castelli, M. Gameiro and J.-P. Lessard
    Archive for Rational Mechanics and Analysis, 228(1):129–157, 2018
    PDF arXiv:1509.08648 Code
  7. [36]
    Continuation of homoclinic orbits in the suspension bridge equation: a computer-assisted proof
    J.B. van den Berg, M. Breden, J.-P. Lessard and M. Murray
    Journal of Differential Equations, 264(5): 3086–3130, 2018
    PDF arXiv:1702.07412

2017

  1. [35]
    Rigorous continuation of bifurcation points in the diblock copolymer equation
    J.-P. Lessard, E. Sander and T. Wanner
    Journal of Computational Dynamics, 4(1-2), 71–118, 2017
    PDF Code
  2. [34]
    Rapidly and slowly oscillating periodic oscillations of a delayed van der Pol oscillator
    G. Kiss and J.-P. Lessard
    Journal of Dynamics and Differential Equations, 29(4): 1233–1257, 2017
    PDF Code
  3. [33]
    Stability and uniqueness of slowly oscillating periodic solutions to Wright's equation
    J. Jaquette, J.-P. Lessard and K. Mischaikow
    Journal of Differential Equations, 263(11): 7263–7286, 2017
    PDF arXiv:1705.02432 Code
  4. [32]
    A framework for the numerical computation and a posteriori verification of invariant objects of evolution equations
    R. de la Llave, J.-L. Figueras, M. Gameiro and J.-P. Lessard
    SIAM Journal on Applied Dynamical Systems 16(2): 1070–1088, 2017
    PDF arXiv:1605.01086
  5. [31]
    A posteriori verification of invariant objects of evolution equations: periodic orbits in the Kuramoto-Sivashinsky PDE
    M. Gameiro and J.-P. Lessard
    SIAM Journal on Applied Dynamical Systems, 16(1): 687–728, 2017
    PDF Code
  6. [30]
    Computer assisted Fourier analysis in sequence spaces of varying regularity
    J.-P. Lessard and J.D. Mireles James
    SIAM Journal on Mathematical Analysis, 49(1), 530–561, 2017
    PDF Code

2016

  1. [29]
    Rigorous verification of saddle-node bifurcations in ODEs
    J.-P. Lessard
    Indagationes Mathematicae, 27(4): 1013–1026, 2016
    PDF Code
  2. [28]
    Automatic differentiation for Fourier series and the radii polynomial approach
    J.-P. Lessard, J.D. Mireles James and J. Ransford
    Physica D, 334: 174–186, 2016
    PDF Code
  3. [27]
    Rigorous numerics for analytic solutions of differential equations: the radii polynomial approach
    A. Hungria, J.-P. Lessard and J.D. Mireles James.
    Mathematics of Computation, 85(299): 1427–1459, 2016
    PDF
  4. [26]
    Computation of smooth manifolds via rigorous multi-parameter continuation in infinite dimensions
    M. Gameiro, J.-P. Lessard and A. Pugliese.
    Foundations of Computational Mathematics, 16(2): 531–575, 2016
    PDF Code
  5. [25]
    Computation of maximal local (un)stable manifold patches by the parameterization method
    M. Breden, J.-P. Lessard and J.D. Mireles James.
    Indagationes Mathematicae, 27(1): 340–367, 2016
    PDF arXiv:1508.02615 Code
  6. [24]
    Rigorous numerics for piecewise-smooth systems: a functional analytic approach based on Chebyshev series
    M. Gameiro, J.-P. Lessard and Y. Ricaud
    Journal of Computational and Applied Mathematics, 292, 654–673, 2016
    PDF

2015

  1. [23]
    Analytic enclosure of the fundamental matrix solution
    R. Castelli, J.-P. Lessard and J.D. Mireles James
    Applications of Mathematics, 60(6): 617–636, 2015
    PDF
  2. [22]
    Rigorous numerics in dynamics
    J.B. van den Berg and J.-P. Lessard.
    Notices of the American Mathematical Society, 62(9): 1057–1061, 2015
    PDF
  3. [21]
    Stationary coexistence of hexagons and rolls via rigorous computations
    J.B. van den Berg, A. Deschênes, J.-P. Lessard and J.D. Mireles James
    SIAM Journal on Applied Dynamical Systems, 14 (2), 942–979, 2015
    PDF Code
  4. [20]
    Blow-up profile for solutions of a fourth order nonlinear equation
    L. D'Ambrosio, J.-P. Lessard and A. Pugliese
    Nonlinear Analysis: Theory, Methods and Applications, 121, 280–335, 2015
    PDF Code
  5. [19]
    Rigorous numerics for nonlinear operators with tridiagonal dominant linear parts
    M. Breden, L. Desvillettes and J.-P. Lessard
    Discrete and Continuous Dynamical Systems - Series A, 35 (10), 4765–4789, 2015
    PDF arXiv:1503.06315 Code
  6. [18]
    Parameterization of invariant manifolds for periodic orbits (I): efficient numerics via the Floquet normal form
    R. Castelli, J.-P. Lessard and J.D. Mireles James.
    SIAM Journal on Applied Dynamical Systems, 14(1), 132–167, 2015
    PDF Code
  7. [17]
    Coexistence of nontrivial solutions of the one-dimensional Ginzburg-Landau equation: a computer-assisted proof
    A. Correc and J.-P. Lessard.
    European Journal of Applied Mathematics, 26(1): 33–60, 2015
    PDF Code

2014

  1. [16]
    Computer assisted proof of transverse saddle-to-saddle connecting orbits for first order vector fields
    J.-P. Lessard, J.D. Mireles James and C. Reinhardt.
    Journal of Dynamics and Differential Equations, 26(2): 267–313, 2014
    PDF
  2. [15]
    Rigorous numerics for nonlinear differential equations using Chebyshev series
    J.-P. Lessard and C. Reinhardt.
    SIAM Journal on Numerical Analysis, 52(1): 1–22, 2014
    PDF Code

2013

  1. [14]
    Global bifurcation diagram of steady states of systems of PDEs via rigorous numerics: a 3-component reaction-diffusion system
    M. Breden, J.-P. Lessard and M. Vanicat
    Acta Mathematicae Applicandae, 128(1): 113–152, 2013
    PDF arXiv:1511.01414
  2. [13]
    A method to rigorously enclose eigenpairs of complex interval matrices
    R. Castelli and J.-P. Lessard.
    Applications of Mathematics 2013. Institute of Mathematics, Academy of Sciences of the Czech Republic, Prague, 2013. ISBN 978-80-85823-61-5
    PDF arXiv:1112.5052
  3. [12]
    Rigorous numerics in Floquet theory: computing stable and unstable bundles of periodic orbits
    R. Castelli and J.-P. Lessard
    SIAM Journal on Applied Dynamical Systems, 12 (1): 204–245, 2013
    PDF arXiv:1112.4874
  4. [11]
    Efficient rigorous numerics for higher-dimensional PDEs via one-dimensional estimates
    M. Gameiro and J.-P. Lessard
    SIAM Journal on Numerical Analysis, 51(4), 2063–2087, 2013
    PDF

2012

  1. [10]
    Computational fixed point theory for differential delay equations with multiple time lags
    G. Kiss and J.-P. Lessard
    Journal of Differential Equations, 252 (4): 3093–3115, 2012
    PDF

2011

  1. [9]
    Rigorous numerics for symmetric connecting orbits: even homoclinics of the Gray-Scott equation
    J.B. van den Berg, J.-P. Lessard, J.D. Mireles James and K. Mischaikow
    SIAM Journal on Mathematical Analysis, 43 (4): 1557–1594, 2011
    PDF
  2. [8]
    Existence of secondary bifurcations or isolas for PDEs
    M. Gameiro and J.-P. Lessard
    Nonlinear Analysis: Theory, Methods and Applications, 74 (12): 4131–4137, 2011
    PDF
  3. [7]
    Rigorous computation of smooth branches of equilibria for the three-dimensional Cahn-Hilliard equation
    M. Gameiro and J.-P. Lessard
    Numerische Mathematik, 117 (4): 753–778, 2011
    PDF

2010

  1. [6]
    Analytic estimates and rigorous continuation for equilibria of higher-dimensional PDEs
    M. Gameiro and J.-P. Lessard
    Journal of Differential Equations, 249 (9): 2237–2268, 2010
    PDF
  2. [5]
    Global smooth solution curves using rigorous branch following
    J.B. van den Berg, J.-P. Lessard and K. Mischaikow
    Mathematics of Computation, 79 (271), 1565–1584, 2010
    PDF
  3. [4]
    Recent advances about the uniqueness of the slowly oscillating periodic solutions of Wright's equation
    J.-P. Lessard
    Journal of Differential Equations, 248 (5): 992–1016, 2010
    PDF arXiv:0909.4107

2008

  1. [3]
    Chaotic braided solutions via rigorous numerics: chaos in the Swift-Hohenberg equation
    J.B. van den Berg and J.-P. Lessard
    SIAM Journal on Applied Dynamical Systems, 7(3): 988–1031, 2008
    PDF
  2. [2]
    Validated continuation over large parameter ranges for equilibria of PDEs
    M. Gameiro, J.-P. Lessard and K. Mischaikow
    Mathematics and Computers in Simulation, 79 (4), 1368–1382, 2008
    PDF

2007

  1. [1]
    Validated continuation for equilibria of PDEs
    S. Day, J.-P. Lessard and K. Mischaikow
    SIAM Journal on Numerical Analysis, 45 (4), 1398–1424, 2007
    PDF

Books

Theses