title: Nonlinear relativistic and quantum equations with a common type of solution.
abstract: Generalizations of the three main equations of quantum physics, namely, the Schrödinger, Klein-Gordon, and Dirac equations, are proposed. Nonlinear terms, characterized by exponents depending on an index q, are considered in such a way that the standard linear equations are recovered in the limit q→1. Interestingly, these equations present a common, solitonlike, traveling solution, which is written in terms of the q-exponential function that naturally emerges within nonextensive statistical mechanics. In all cases, the well-known Einstein energy-momentum relation is preserved for arbitrary values of q.
authors.affiliation: Centro Brasileiro de Pesquisas Físicas and National Institute of Science and Technology for Complex Systems, Rua Xavier Sigaud 150, 22290-180 Rio de Janeiro-RJ Brazil. fdnobre@cbpf.br
authors.forename: F D
authors.initials: FD
authors.lastname: Nobre
authors.forename: M A
authors.initials: MA
authors.lastname: Rego-Monteiro
authors.forename: C
authors.initials: C
authors.lastname: Tsallis