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 $q\to 1$. Interestingly, these equations present a common, soliton-like, travelling 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 $q$.

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Cited by in corpus (53)

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• From the hypergeometric differential equation to a non linear Schrödinger one
• Nonextensive Nuclear Liquid-Gas Phase Transition
• Conceptual Inadequacy of the Shore and Johnson Axioms for Wide Classes of Complex Systems
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• Inter-occurrence times and universal laws in finance, earthquakes and genomes
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