Quase-integrabilidade em modelos holônomos e não-holônomos de tipo seno-Gordon deformado : equação de Riccati e novas cargas conservadas

Abstract

In this work, we will study some properties of deformed sine-Gordon models in the context of the concept of quasi-integrability. We calculate an infinite number of new quasiconserved quantities through a modification of the usual techniques of integrable field theories. That is, we use the anomalous Lax equations, the linear problem associated and its Riccati type equations. We have performed numerical simulations for the first non-trivial charge and its associated anomalies for collisions of kink-kink, kink-antikink and breathers. Besides, we consider the sine-Gordon model of variable velocity and mass (VMSG) in the formulation of Kac-Moody algebra. We study the gauge transformations in a process of “abelianization” of the Lax connections in order to obtain quasi-conservation laws and their associated charges and anomalies.