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Nonlinear waves in a simple model of high-grade glioma

Arturo Álvarez-Arenas

Arturo Álvarez-Arenas

Department of Mathematics and Mathematical Oncology Laboratory, University of Castilla-La ManchaCiudad Real, Spain
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Álvarez-Arenas, Arturo
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Juan Belmonte-Beitia

Juan Belmonte-Beitia

Department of Mathematics and Mathematical Oncology Laboratory, University of Castilla-La ManchaCiudad Real, Spain
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Belmonte-Beitia, Juan
 e 
Gabriel F. Calvo

Gabriel F. Calvo

Department of Mathematics and Mathematical Oncology Laboratory, University of Castilla-La ManchaCiudad Real, Spain
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Calvo, Gabriel F.
  
01 ott 2016
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Pubblicato online: 01 ott 2016
Pagine: 405 - 422
Ricevuto: 15 mag 2016
Accettato: 01 ott 2016
DOI: https://doi.org/10.21042/AMNS.2016.2.00035
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© 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.

Fig. 1

(a) Heteroclinic orbits of Eq. (10) for β = 0.1. (b) Kink solution for β = 0.1 corresponding to the marked heteroclinic orbit in (a). (c) The bright soliton solution 𝓤 corresponds to the kink obtained in (b)
(a) Heteroclinic orbits of Eq. (10) for β = 0.1. (b) Kink solution for β = 0.1 corresponding to the marked heteroclinic orbit in (a). (c) The bright soliton solution 𝓤 corresponds to the kink obtained in (b)

Fig. 2

Bright solitary waves for β = 0.3, ϕ0 = 0.5 and c = 2.5. (a) Profiles from Eq. (45) (solid curve) and the explicit solution given by Eq. (46) (dashed curve). (b) Homoclinic orbits from Eq. (45) (solid curve) and Eq. (46) (dashed curve).
Bright solitary waves for β = 0.3, ϕ0 = 0.5 and c = 2.5. (a) Profiles from Eq. (45) (solid curve) and the explicit solution given by Eq. (46) (dashed curve). (b) Homoclinic orbits from Eq. (45) (solid curve) and Eq. (46) (dashed curve).

Fig. 3

Characteristic curves of the minimum speed c0 for positive bright solitary solutions, in terms of (a) β and (b) ϕ0, calculated from Eq. (53).
Characteristic curves of the minimum speed c0 for positive bright solitary solutions, in terms of (a) β and (b) ϕ0, calculated from Eq. (53).

Fig. 4

Plot of the depth of resection b versus the recurrence time t for different values of the proliferation rate: ρ = 1/5 (blue solid line), ρ = 1/4 (green dashed line) and ρ = 1/3 (red dotted-dashed line).
Plot of the depth of resection b versus the recurrence time t for different values of the proliferation rate: ρ = 1/5 (blue solid line), ρ = 1/4 (green dashed line) and ρ = 1/3 (red dotted-dashed line).
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Inglese
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Scienze biologiche, Scienze della vita, altro, Matematica, Matematica applicata, Matematica generale, Fisica, Fisica, altro
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