Related papers: A non-monotone conservation law for dune morphodyn…
The conservation laws of electromagnetism, and implicitly all theories built from quadratic Lagrangians, are extended to a continuum of nonlocal versions. These are associated with symmetries of a class of equal time field correlation…
Noether's theorem connects symmetries to invariants in continuous systems, however its extension to discrete systems has remained elusive. Recognizing the lowest-order finite difference as the foundation of local continuity, a viable method…
Conservation laws are well-established in the context of Euclidean gradient flow dynamics, notably for linear or ReLU neural network training. Yet, their existence and principles for non-Euclidean geometries and momentum-based dynamics…
In an earlier work by a subset of the present authors, the method of the so-called neural deflation was introduced towards identifying a complete set of functionally independent conservation laws of a nonlinear dynamical system. Here, we…
Using a general theorem on conservation laws for arbitrary differential equations proved by Ibragimov, we have derived conservation laws for Dirac's symmetrized Maxwell-Lorentz equations under the assumption that both the electric and…
In recent work we constructed completely general conservation laws for energy and linear and angular momentum of extended systems in general relativity based on the notion of a rigid quasilocal frame (RQF). We argued at a fundamental level…
For nonlinear Schr\"odinger equations in less than or equal to four dimension, with non-vanishing initial data at infinity, a new approach to derive the conservation law is obtained. Since this approach does not contain approximating…
The concept of nonlinear self-adjointness is employed to construct the conservation laws for fractional evolution equations using its Lie point symmetries. The approach is demonstrated on subdiffusion and diffusion-wave equations with the…
We use the Lagrange-Noether methods to derive the conservation laws for models in which matter interacts nonminimally with the gravitational field. The nonminimal coupling function can depend arbitrarily on the gravitational field strength.…
In the paper the role of conservation laws in evolutionary processes, which proceed in material systems (in material media) and lead to generation of physical fields, is shown using skew-symmetric differential forms. In present paper the…
We derive the Noether identities and the conservation laws for general gravitational models with arbitrarily interacting matter and gravitational fields. These conservation laws are used for the construction of the covariant equations of…
Nonlocal conservation laws are used to describe various realistic instances of crowd behaviors. First, a basic analytic framework is established through an "ad hoc" well posedness theorem for systems of nonlocal conservation laws in several…
We examine conservation laws, typically the conservation of linear momentum, in the light of a recent successful formulation of fermions as Kerr-Newman type Black Holes, which are created fluctuationally from a background Zero Point Field.…
Conservation laws are an inherent feature in many systems modeling real world phenomena, in particular, those modeling biological and chemical systems. If the form of the underlying dynamical system is known, linear algebra and algebraic…
We use the general theory of local conservation laws for arbitrary partial differential equations to provide a geometric framework for conservation laws on characteristic null hypersurfaces. The operator of interest is the wave operator on…
Conservation laws are computed for various nonlinear partial differential equations that arise in elasticity and acoustics. Using a scaling homogeneity approach, conservation laws are established for two models describing shear wave…
In the work it has been shown that there are two types of the conservation laws. 1. The conservation laws that can be called exact ones. They point to an avalability of some conservative quantities or objects. Such objects are the physical…
In the process of the deep learning, we integrate more integrable information of nonlinear wave models, such as the conservation law obtained from the integrable theory, into the neural network structure, and propose a conservation-law…
It can be agreed that the linear superposition and energy conservation are two independent physics laws in general. The former allows the energy to be re-distributed over space and the latter restricts the energy in the total amount.…
The system of equations of one-dimensional shallow water over uneven bottom in Euler's and Lagrange's variables is considered. Intermediate system of equations is introduced. Hydrodynamic conservation laws of intermediate system of…