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math.AP2020
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…
math.DS2020
Validated Numerical Approximation of Stable Manifolds for Parabolic Partial Differential Equations
Jan Bouwe van den Berg, Jonathan Jaquette, J. D. Mireles James
This paper develops validated computational methods for studying infinite dimensional stable manifolds at equilibrium solutions of parabolic PDEs, synthesizing disparate errors res…