A detailed examination of the infinite dimensional loop algebra of hidden symmetry transformations of the Principal Chiral Model reveals it to have a structure differing from a standard centreless Kac-Moody algebra. A new infinite dimensional abelian symmetry algebra is shown to preserve a symplectic form on the space of solutions. 1. We have recently obtained [1] a novel free-field parametrisa...

In this paper, Heir-equations method is applied to investigate nonclassical symmetries and new solutions of the Black-Scholes equation. Nonlinear self-adjointness is proved and infinite number of conservation laws are computed by a new conservation laws theorem.

Abstract In both quantum and classical field systems, conservation laws such as the of energy momentum are widely regarded fundamental properties. A broadly accepted approach to deriving is built using Noether’s method. However, this procedure still unclear for relativistic particle-field systems where particles world lines. present study, we establish a general manifestly covariant or geometri...