Shadowing of non-transversal heteroclinic chains
Amadeu Delshams, Adri\`a Simon, Piotr Zgliczy\'nski
TL;DR
This paper introduces a novel shadowing mechanism for nontransversal heteroclinic chains using dimension dropping, demonstrated through examples and applied to a simplified nonlinear Schrödinger equation model.
Contribution
It presents a new shadowing approach for nontransversal heteroclinic chains based on dropping dimensions, with applications to a toy model of nonlinear Schrödinger equations.
Findings
New shadowing mechanism for nontransversal chains
Illustrative examples demonstrating the mechanism
Application to a simplified nonlinear Schrödinger model
Abstract
We present a new result about the shadowing of nontransversal chain of heteroclinic connections based on the idea of dropping dimensions. We illustrate this new mechanism with several examples. As an application we discuss this mechanism in a simplification of a toy model system derived by Colliander et al. in the context of cubic defocusing nonlinear Schr\"odinger equation.
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Taxonomy
TopicsNonlinear Dynamics and Pattern Formation · Nonlinear Photonic Systems · Nonlinear Waves and Solitons