Generalized and new solutions of the NRT nonlinear Schrödinger equation

Abstract

In this paper we present new solutions of the non-linear Schröodinger equation proposed by Nobre, Rego-Monteiro and Tsallis for the free particle, obtained from different Lie symmetry reductions. Analytical expressions for the wave function, the auxiliary field and the probability density are derived using a variety of approaches. Solutions involving elliptic functions, Bessel and modified Bessel functions, as well as the inverse error function are found, amongst others. On the other hand, a closed-form expression for the general solution of the traveling wave ansatz (see Bountis and Nobre) is obtained for any real value of the nonlinearity index. This is achieved through the use of the so-called generalized trigonometric functions as defined by Lindqvist and Drábek, the utility of which in analyzing the equation under study is highlighted throughout the paper.

References in corpus (5)

• Analytical solutions for problems of bubble dynamics
• Analytical solutions of the Rayleigh equation for empty and gas--filled bubble
• On Generalized Stam Inequalities and Fisher-Rényi Complexity Measures
• Applications of a duality between generalized trigonometric and hyperbolic functions II
• Lorentzian Solitary Wave in a Generalised Nonlinear Schrödinger Equation