A family of nonlinear Schrodinger equations admitting q-plane wave solutions

作者：Nobre F D; Plastino A R^*

来源：Physics Letters A, 2017, 381(31): 2457-2462.

DOI：10.1016/j.physleta.2017.05.054

• Nonlinear Schrodinger equations
• Classical field theory
• Nonextensive thermostatistics
• Nonadditive entropies

Nonlinear Schrodinger equations with power-law nonlinearities have attracted considerable attention recently. Two previous proposals for these types of equations, corresponding respectively to the Gross-Pitaievsky equation and to the one associated with nonextensive statistical mechanics, are here unified into a single, parameterized family of nonlinear Schrodinger equations. Power-law nonlinear terms characterized by exponents depending on a real index q, typical of nonextensive statistical mechanics, are considered in such a way that the Gross-Pitaievsky equation is recovered in the limit q -> 1. A classical field theory shows that, due to these nonlinearities, an extra field phi((x) over right arrow ,t) (besides the usual one Psi((x) over right arrow ,t)) must be introduced for consistency. The new field can be identified with Psi*((x) over right arrow ,t) only when q -> 1. For q not equal 1 one has a pair of coupled nonlinear wave equations governing the joint evolution of the complex valued fields Psi((x) over right arrow ,t) and phi((x) over right arrow ,t). These equations reduce to the usual pair of complex-conjugate ones only in the q -> 1 limit. Interestingly, the nonlinear equations obeyed by Psi((x) over right arrow ,t) and phi((x) over right arrow ,t) exhibit a common, soliton-like, traveling solution, which is expressible in terms of the q-exponential function that naturally emerges within nonextensive statistical mechanics.

• 出版日期2017-8-21