solitons in nonlinear deformable systems with impurities

The purpose of this thesis is the study of the influence of impurities on the nucleation rate of kink-antikink pairs in nonlinear deformable systems. We study the dynamics of solitary waves in the generalized Frenkel-Kontorova (GFK) model, discussed about kink profiles and energy in the continuum limit of this model and present Some conclusions concerning the interactions of kink in the system.The influence of the Gaussian approximation on the nucleation rate of kink-antikink pairs in a nonlinear deformable chain is performed and a new formula for the nucleation rate of kink-antikink pairs is determined. Using the Kolmogorov method in the GFK model in the presence of external forces and impurities, we set off analytical expression of the nucleation rate in the system. A Numerical application of this theory is made by using existing data. We end by investigating the role of the applied field on the nucleation process in an inhomogeneous deformable chain. The Hamiltonian formalism allows us to model the system. We derive numerically the depinning threshold field of the system and show the influence of the deformability of the impurity potential on this depinning threshold field.