Skip to Main content Skip to Navigation
Journal articles

Bifurcations of Phase Portraits of a Singular Nonlinear Equation of the Second Class

Abstract : The soliton dynamics is studied using the Frenkel Kontorova (FK) model with non- convex interparticle interactions immersed in a parameter ized on-site substrate po- tential. The case of a deformable substrate potential allow s theoretical adaptation of the model to various physical situations. Non-convex inter actions in lattice systems lead to a number of interesting phenomena that cannot be prod uced with linear coupling alone. In the continuum limit for such a model, the p articles are governed by a Singular Nonlinear Equation of the Second Class. The dyn amical behavior of traveling wave solutions is studied by using the theory of bi furcations of dynamical systems. Under different parametric situations, we give vari ous sufficient conditions leading to the existence of propagating wave solutions or di slocation threshold, high- lighting namely that the deformability of the substrate pot ential plays only a minor role.
Complete list of metadatas

Cited literature [15 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-00934971
Contributor : Jean-Marie Bilbault <>
Submitted on : Wednesday, January 22, 2014 - 8:16:11 PM
Last modification on : Monday, March 30, 2020 - 8:44:48 AM
Document(s) archivé(s) le : Thursday, April 24, 2014 - 11:30:47 AM

File

Nguetcho_Article_CNSNS.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-00934971, version 1

Citation

Aurélien Serge Tchakoutio Nguetcho, Jibin Li, Jean-Marie Bilbault. Bifurcations of Phase Portraits of a Singular Nonlinear Equation of the Second Class. Communications in Nonlinear Science and Numerical Simulation, Elsevier, 2014, http://dx.doi.org/10.1016/j.cnsns.2013.12.022. ⟨hal-00934971⟩

Share

Metrics

Record views

467

Files downloads

588