<abstract xmlns="http://www.w3.org/1999/xhtml"><p>We present an analysis of a mathematical model describing the key features of the most frequent and aggressive type of primary brain tumor: glioblastoma. The model captures the salient physiopathological characteristics of this type of tumor: invasion of the normal brain tissue, cell proliferation and the formation of a necrotic core. Our study, based on phase space analysis, geometric perturbation theory, exact solutions and numerical simulations, proves the existence of bright solitary waves in the tumor coupled with kink and anti-kink fronts for the normal tissue and the necrotic core. Finally, we study the linear stability of the solutions to calculate the time of tumor recurrence.</p></abstract>

We present an analysis of a mathematical model describing the key features of the most frequent and aggressive type of primary brain tumor: glioblastoma. The model captures the salient physiopathological characteristics of this type of tumor: invasion of the normal brain tissue, cell proliferation and the formation of a necrotic core. Our study, based on phase space analysis, geometric perturbation theory, exact solutions and numerical simulations, proves the existence of bright solitary waves in the tumor coupled with kink and anti-kink fronts for the normal tissue and the necrotic core. Finally, we study the linear stability of the solutions to calculate the time of tumor recurrence.

Nonlinear waves in a simple model of high-grade glioma

Department of Mathematics and Mathematical Oncology Laboratory

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Nonlinear waves in a simple model of high-grade glioma"}

We present an analysis of a mathematical model describing the key features of the most frequent and aggressive type of primary brain tumor: glioblastoma. The...

Nonlinear waves in a simple model of high-grade glioma

Published Online: Oct 01, 2016

Page range: 405 - 422

Received: May 15, 2016

Accepted: Oct 01, 2016

DOI: https://doi.org/10.21042/AMNS.2016.2.00035

Keywords
Solitary waves, bright solitons, dark solitons, mathematical oncology

© 2016 Arturo Álvarez-Arenas, Juan Belmonte-Beitia, and Gabriel F. Calvo, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Nonlinear waves in a simple model of high-grade glioma

Published Online: Oct 01, 2016

Page range: 405 - 422

Received: May 15, 2016

Accepted: Oct 01, 2016

DOI: https://doi.org/10.21042/AMNS.2016.2.00035

KeywordsSolitary waves, bright solitons, dark solitons, mathematical oncology

© 2016 Arturo Álvarez-Arenas, Juan Belmonte-Beitia, and Gabriel F. Calvo, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Solitary waves, bright solitons, dark solitons, mathematical oncology