This paper presents an epistemological analysis of the search for new conservation laws in particle physics. Discovering conservation laws has posed various challenges concerning the underdetermination of theory by evidence, to which physicists have found various responses. These responses include an appeal to a plenitude principle, a maxim for inductive inference, looking for a parsimonious sy...

This paper presents an epistemological analysis of the search for new conservation laws in particle physics. Discovering conservation laws has posed various challenges concerning the underdetermination of theory by evidence, to which physicists have found various responses. These responses include an appeal to a plenitude principle, a maxim for inductive inference, looking for a parsimonious sy...

The classical generation theorem of conservation laws from known ones for a system of differential equations which uses the action of a canonical Lie–Bäcklund generator is extended to include any Lie–Bäcklund generator. Also, it is shown that the Lie algebra of Lie–Bäcklund symmetries of a conserved vector of a system is a subalgebra of the Lie–Bäcklund symmetries of the system. Moreover, we in...

Conservation laws of third order quasi-linear scalar evolution equations are studied via exterior differential system and characteristic cohomology. We find a subspace of 2-forms in the infinite prolongation space in which every conservation law has a unique representative. Analysis of the structure of this subspace based upon the symbol of the differential equation leads to a universal integra...

Each conservation law of a given partial differential equation is determined (up to equivalence) by a function known as the characteristic. This function is used to find conservation laws, to prove equivalence between conservation laws, and to prove the converse of Noether’s Theorem. Transferring these results to difference equations is nontrivial, largely because difference operators are not d...

We consider the Cauchy problem for a degenerate fractional conservation laws driven by noise. In particular, making use of an adapted kinetic formulation, result existence and uniqueness solution is established. Moreover, unified framework also established to develop continuous dependence theory. More precisely, we demonstrate $$L^1$$ -continuous estimates on initial data, order Laplacian, diff...