2 citations · 3 across the 3 of their papers we have counts for
5 papers
Global dynamics in nonconservative nonlinear Schrödinger equations
Jonathan Jaquette, Jean-Philippe Lessard, Akitoshi Takayasu
In this paper, we study the global dynamics of a class of nonlinear Schrödinger equations using perturbative and non-perturbative methods. We prove the semi-global existence of sol…
Rigorous numerics for nonlinear heat equations in the complex plane of time
Akitoshi Takayasu, Jean-Philippe Lessard, Jonathan Jaquette +1
In this paper, we introduce a method for computing rigorous local inclusions of solutions of Cauchy problems for nonlinear heat equations for complex time values. Using a solution…
Fractal Dimension Estimation with Persistent Homology: A Comparative Study
Jonathan Jaquette, Benjamin Schweinhart
We propose that the recently defined persistent homology dimensions are a practical tool for fractal dimension estimation of point samples. We implement an algorithm to estimate th…
A proof of Jones' conjecture
Jonathan Jaquette
In this paper, we prove that Wright's equation has a unique slowly oscillating periodic solution for parameter values , up…
Stability and Uniqueness of Slowly Oscillating Periodic Solutions to Wright's Equation
Jonathan Jaquette, Jean-Philippe Lessard, Konstantin Mischaikow
In this paper, we prove that Wright's equation has a unique slowly oscillating periodic solution (SOPS) for all parameter values ,…