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arXiv · 2109.00159

Singularities and heteroclinic connections in complex-valued evolutionary equations with a quadratic nonlinearity

Jonathan Jaquette·Jean-Philippe Lessard·Akitoshi Takayasu
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Abstract

In this paper, we consider the dynamics of solutions to complex-valued evolutionary partial differential equations (PDEs) and show existence of heteroclinic orbits from nontrivial equilibria to zero via computer-assisted proofs. We also show that the existence of unbounded solutions along unstable manifolds at the equilibrium follows from the existence of heteroclinic orbits. Our computer-assisted proof consists of three separate techniques of rigorous numerics: an enclosure of a local unstable manifold at the equilibria, a rigorous integration of PDEs, and a constructive validation of a trapping region around the zero equilibrium.

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Jonathan Jaquette, Jean-Philippe Lessard, Akitoshi Takayasu. 2021-09-01. Singularities and heteroclinic connections in complex-valued evolutionary equations with a quadratic nonlinearity. https://doi.org/10.1016/j.cnsns.2021.106188

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