Noether Symmetries Quantization and Superintegrability of Biological Models

Abstract

It is shown that quantization and superintegrability are not concepts that are inherent to classical Physics alone. Indeed, one may quantize and also detect superintegrability of biological models by means of Noether symmetries. We exemplify the method by using a mathematical model that was proposed by Basener and Ross (2005), and that describes the dynamics of growth and sudden decrease in the population of Easter Island.

Moving energies hide within Noether’s first theorem

“…the difference between kinetic energy and potential energy, then E L is not the mechanical energy. However, E L may correspond to the Hamiltonian that can be obtained by applying Legendre transformation to L. An example can be found in [22]. Moreover, the nonuniqueness of the Lagrangian 6 suggests to look for a Lagrangian L = L(t, q, _ q) that admits the maximal number of Noether point symmetries [11,12], i.e.…”

Fourth-Order Pattern Forming Pdes: Partial and Approximate Symmetries

“…In the past, solutions of these and related equations have been found using numerical methods, see [5,16] and references therein. Recent studies involving conservation laws and symmetries have provided interesting results for stream functions [10], beams [13], biological models [21], nonlinear systems [2] and diffusion equations [11].…”

Lie symmetries and singularity analysis for generalized shallow-water equations

“…The are many applications of the Lie symmetries on the analysis of differential equations, for the determination of exact solutions, to determine conservation laws, study the integrability of dynamical systems or classify algebraic equivalent systems [6][7][8][9][10][11][12][13]. Integrability is a very important property of dynamical systems, hence it worth to investigate if a given dynamical system is integrable [14][15][16][17][18][19][20][21].…”