0000000000965187
AUTHOR
Jibin Li
Global dynamical behaviors in a physical shallow water system
International audience; The theory of bifurcations of dynamical systems is used to investigate the behavior of travelling wave solutions in an entire family of shallow water wave equations. This family is obtained by a perturbative asymptotic expansion for unidirectional shallow water waves. According to the parameters of the system, this family can lead to different sets of known equations such as Camassa-Holm, Korteweg-de Vries, Degasperis and Procesi and several other dispersive equations of the third order. Looking for possible travelling wave solutions, we show that different phase orbits in some regions of parametric planes are similar to those obtained with the model of the pressure …
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 parameterized on-site substrate potential. The case of a deformable substrate potential allows theoretical adaptation of the model to various physical situations. Non-convex interactions in lattice systems lead to a number of interesting phenomena that cannot be produced with linear coupling alone. In the continuum limit for such a model, the particles are governed by a Singular Nonlinear Equation of the Second Class. The dynamical behavior of traveling wave solutions is studied by using the theory of bifurcations of dynamical systems. Under different para…
Bifurcations of Phase Portraits of a Singular Nonlinear Equation of the Second Class
International audience; 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 syst…