Dual conservation laws of linear planar elasticity theory have been systematically studied based on stress function formalism. By employing generalized symmetry transformation or Lie–B€acklund transformation, a class of new dual conservation laws in planar elasticity have been discovered based on Noether theorem and its Bessel–Hagen generalization. These dual conservation laws represent variati...

Evidence and results suggesting that a Noether–like theorem for conservation laws in 1D RCA can be obtained. Unlike Noether’s theorem, the connection here is to the maximal congruences rather than the automorphisms of the local dynamics. We take the results of Takesue and Hattori (1992) on the space of additive conservation laws in one dimensional cellular automata. In reversible automata, we s...

We introduce notions of equivalence of conservation laws with respect to Lie symmetry groups for fixed systems of differential equations and with respect to equivalence groups or sets of admissible transformations for classes of such systems. We also revise the notion of linear dependence of conservation laws and define the notion of local dependence of potentials. To construct conservation law...

Abstract: A conservation law theorem stated by N. Ibragimov along with its subsequent extensions are shown to be a special case of a standard formula that uses a pair consisting of a symmetry and an adjoint-symmetry to produce a conservation law through a well-known Fréchet derivative identity. Furthermore, the connection of this formula (and of Ibragimov’s theorem) to the standard action of sy...

This is an introductory survey of the theory of p-form conservation laws in field theory. It is based upon a series of lectures given at the Second Mexican School on Gravitation and In these lectures I will provide a survey of some aspects of the theory of local coho-mology in field theory and provide some illustrative applications, primarily taken from the Einstein equations of the general the...

We study higher-order conservation laws of the non-linearizable elliptic Poisson equation ∂ 2 u ∂z∂z = −f(u) as elements of the characteristic cohomology of the associated exterior differential system. The theory of characteristic cohomology determines a normal form for differentiated conservation laws by realizing them as elements of the kernel of a linear differential operator. The S1–symmetr...

A direct approach is proposed for constructing conservation laws of discrete evolution equations, regardless of the existence of a Lagrangian. The approach utilizes pairs of symmetries and adjoint symmetries, in which adjoint symmetries make up for the disadvantage of non-Lagrangian structures in presenting a correspondence between symmetries and conservation laws. Applications are made for the...

On the basis of the integral theorems about the mean curvature and Gauss curvature, geometric conservation laws for cells or vesicles are proved. These conservation laws may depict various special bionano structures discovered in experiments, such as the membrane nanotubes and singular points grown from the surfaces of cells or vesicles. Potential applications of the conservation laws to lipid ...

Generalizing results by Bryant and Griffiths [Duke Math. J., 1995, V.78, 531–676], we completely describe local conservation laws of second-order (1 + 1)-dimensional evolution equations up to contact equivalence. The possible dimensions of spaces of conservation laws prove to be 0, 1, 2 and infinity. The canonical forms of equations with respect to contact equivalence are found for all nonzero ...

Conservation tillage (CT) systems have a number of potential benefits including lower crop production costs and the ability to reduce soil erosion that have made them common in several regions of the world. Although CT systems have been researched and successfully implemented on some farms in California's San Joaquin Valley (SJV), overall adoption is low and the reasons for the region's compara...