Non-synchronized solutions to nonlinear elliptic Schrödinger systems on a closed Riemannian manifold

Saikat Mazumdar; Jérôme Vétois

doi:10.3934/dcds.2022097

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2022, Volume 42, Issue 11: 5273-5287. Doi: 10.3934/dcds.2022097

This issue Previous Article Long exact sequences of homology groups of étale groupoids Next Article Fiber entropy and algorithmic complexity of random orbits

Non-synchronized solutions to nonlinear elliptic Schrödinger systems on a closed Riemannian manifold

Saikat Mazumdar^1, and
Jérôme Vétois^2,

1.
Department of Mathematics, Indian Institute of Technology Bombay, Powai, Mumbai 400076, Maharashtra, India
2.
Department of Mathematics and Statistics, McGill University, 805 Sherbrooke Street West, Montreal, Quebec H3A 0B9, Canada

Received: March 2022

Early access: July 2022

Published: November 2022

The second author was supported by the Discovery Grant RGPIN-2016-04195 from the Natural Sciences and Engineering Research Council of Canada. This work was partially conducted when the first author held a postdoctoral position at McGill University under the co-supervision of Professors Pengfei Guan, Niky Kamran and the second author, that was supported by the NSERC Discovery Grants RGPIN-04443-2018, RGPIN-05490-2018 and RGPIN-04195-2016.

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Abstract

On a smooth, closed Riemannian manifold, we study the question of proportionality of components, also called synchronization, of vector-valued solutions to nonlinear elliptic Schrödinger systems with constant coefficients. In particular, we obtain bifurcation results showing the existence of branches of non-synchronized solutions emanating from the constant solutions.

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Mathematics Subject Classification: Primary: 35J47, 35B32; Secondary: 35J10, 58J05.

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