Validated Continuation for Equilibria of PDEs. - Sarah Day; Jean-Philippe Lessard; Konstantin Mischaikow (SIAM J. Numer. Anal., 2007)

Validated continuation over large parameter ranges for equilibria of PDEs. - Marcio Gameiro; Jean-Philippe Lessard; Konstantin Mischaikow (Math. Comput. Simul., 2008)

Chaotic Braided Solutions via Rigorous Numerics: Chaos in the Swift-Hohenberg Equation. - Jan Bouwe van den Berg; Jean-Philippe Lessard (SIAM J. Appl. Dyn. Syst., 2008)

Global smooth solution curves using rigorous branch following. - Jan Bouwe van den Berg; Jean-Philippe Lessard; Konstantin Mischaikow (Math. Comput., 2010)

Rigorous computation of smooth branches of equilibria for the three dimensional Cahn-Hilliard equation. - Marcio Gameiro; Jean-Philippe Lessard (Numerische Mathematik, 2011)

Rigorous Numerics for Symmetric Connecting Orbits: Even Homoclinics of the Gray-Scott Equation. - Jan Bouwe van den Berg; Jason D. Mireles-James; Jean-Philippe Lessard; Konstantin Mischaikow (SIAM J. Math. Anal., 2011)

Rigorous Numerics in Floquet Theory: Computing Stable and Unstable Bundles of Periodic Orbits. - Roberto Castelli; Jean-Philippe Lessard (SIAM J. Appl. Dyn. Syst., 2013)

Efficient Rigorous Numerics for Higher-Dimensional PDEs via One-Dimensional Estimates. - Marcio Gameiro; Jean-Philippe Lessard (SIAM J. Numer. Anal., 2013)

Rigorous Numerics for Nonlinear Differential Equations Using Chebyshev Series. - Jean-Philippe Lessard; Christian Reinhardt (SIAM J. Numer. Anal., 2014)

Stationary Coexistence of Hexagons and Rolls via Rigorous Computations. - Jan Bouwe van den Berg; Andréa Deschênes; Jean-Philippe Lessard; Jason D. Mireles-James (SIAM J. Appl. Dyn. Syst., 2015)

Parameterization of Invariant Manifolds for Periodic Orbits I: Efficient Numerics via the Floquet Normal Form. - Roberto Castelli; Jean-Philippe Lessard; Jason D. Mireles-James (SIAM J. Appl. Dyn. Syst., 2015)

Computation of Smooth Manifolds Via Rigorous Multi-parameter Continuation in Infinite Dimensions. - Marcio Gameiro; Jean-Philippe Lessard; Alessandro Pugliese (Found. Comput. Math., 2016)

Rigorous numerics for piecewise-smooth systems: A functional analytic approach based on Chebyshev series. - Marcio Gameiro; Jean-Philippe Lessard; Yann Ricaud (J. Comput. Appl. Math., 2016)

Rigorous numerics for analytic solutions of differential equations: the radii polynomial approach. - Allan Hungria; Jean-Philippe Lessard; Jason D. Mireles-James (Math. Comput., 2016)

A Framework for the Numerical Computation and A Posteriori Verification of Invariant Objects of Evolution Equations. - Jordi-Lluís Figueras; Marcio Gameiro; Jean-Philippe Lessard; Rafael de la Llave (SIAM J. Appl. Dyn. Syst., 2017)

A Posteriori Verification of Invariant Objects of Evolution Equations: Periodic Orbits in the Kuramoto-Sivashinsky PDE. - Marcio Gameiro; Jean-Philippe Lessard (SIAM J. Appl. Dyn. Syst., 2017)

Computer Assisted Fourier Analysis in Sequence Spaces of Varying Regularity. - Jean-Philippe Lessard; Jason D. Mireles-James (SIAM J. Math. Anal., 2017)

Traveling wave oscillatory patterns in a signed Kuramoto-Sivashinsky equation with absorption. - Yvonne Alama Bronsard; Jean-Philippe Lessard (J. Comput. Appl. Math., 2020)

Free Vibrations in a Wave Equation Modeling MEMS. - Carlos García-Azpeitia; Jean-Philippe Lessard (SIAM J. Appl. Dyn. Syst., 2020)

Microscopic Patterns in the 2D Phase-Field-Crystal Model. - Gabriel Martine-La Boissoniere; Rustum Choksi; Jean-Philippe Lessard (CoRR, 2021)

A geometric characterization of unstable blow-up solutions with computer-assisted proof. - Jean-Philippe Lessard; Kaname Matsue; Akitoshi Takayasu (CoRR, 2021)

Spontaneous Periodic Orbits in the Navier-Stokes Flow. - Jan Bouwe van den Berg; Maxime Breden; Jean-Philippe Lessard; Lennaert van Veen (J. Nonlinear Sci., 2021)

Rigorous Verification of Hopf Bifurcations via Desingularization and Continuation. - Jan Bouwe van den Berg; Jean-Philippe Lessard; Elena Queirolo (SIAM J. Appl. Dyn. Syst., 2021)

Validated forward integration scheme for parabolic PDEs via Chebyshev series. - Jacek Cyranka; Jean-Philippe Lessard (Commun. Nonlinear Sci. Numer. Simul., 2022)

Singularities and heteroclinic connections in complex-valued evolutionary equations with a quadratic nonlinearity. - Jonathan Jaquette; Jean-Philippe Lessard; Akitoshi Takayasu (Commun. Nonlinear Sci. Numer. Simul., 2022)

Rigorous numerics for nonlinear heat equations in the complex plane of time. - Akitoshi Takayasu; Jean-Philippe Lessard; Jonathan Jaquette; Hisashi Okamoto (Numerische Mathematik, 2022)

Correction to: Rigorous numerics for nonlinear heat equations in the complex plane of time. - Akitoshi Takayasu; Jean-Philippe Lessard; Jonathan Jaquette; Hisashi Okamoto (Numerische Mathematik, 2022)

Worrisome Properties of Neural Network Controllers and Their Symbolic Representations. - Jacek Cyranka; Kevin E. M. Church; Jean-Philippe Lessard (ECAI, 2023)

Saddle-Type Blow-Up Solutions with Computer-Assisted Proofs: Validation and Extraction of Global Nature. - Jean-Philippe Lessard; Kaname Matsue; Akitoshi Takayasu (J. Nonlinear Sci., 2023)

Persistence of Periodic Orbits under State-dependent Delayed Perturbations: Computer-assisted Proofs. - Joan Gimeno; Jean-Philippe Lessard; Jason D. Mireles-James; Jiaqi Yang (SIAM J. Appl. Dyn. Syst., 2023)

Numerical Computation of Transverse Homoclinic Orbits for Periodic Solutions of Delay Differential Equations. - Olivier Hénot; Jean-Philippe Lessard; Jason D. Mireles-James (SIAM J. Appl. Dyn. Syst., 2023)

Rigorous Computation of Solutions of Semilinear PDEs on Unbounded Domains via Spectral Methods. - Matthieu Cadiot; Jean-Philippe Lessard; Jean-Christophe Nave (SIAM J. Appl. Dyn. Syst., 2024)

Toward Computational Morse-Floer Homology: Forcing Results for Connecting Orbits by Computing Relative Indices of Critical Points. - Jan Bouwe van den Berg; Marcio Gameiro; Jean-Philippe Lessard; Rob Van der Vorst (Found. Comput. Math., 2024)

Validated matrix multiplication transform for orthogonal polynomials with applications to computer-assisted proofs for PDEs. - Matthieu Cadiot; Jonathan Jaquette; Jean-Philippe Lessard; Akitoshi Takayasu (Commun. Nonlinear Sci. Numer. Simul., 2025)

A Rigorous Integrator and Global Existence for Higher-Dimensional Semilinear Parabolic PDEs via Semigroup Theory. - Gabriel William Duchesne; Jean-Philippe Lessard; Akitoshi Takayasu (J. Sci. Comput., 2025)

From heteroclinic loops to homoclinic snaking in reversible systems: rigorous forcing through computer-assisted proofs. - Jan Bouwe van den Berg; Gabriel William Duchesne; Jean-Philippe Lessard (CoRR, 2025)