A conservation law in a cellular automaton is the statement of the invariance of a local and additive energy-like quantity. This chapter reviews the basic theory of conservation laws in cellular automata. A general mathematical framework for formulating conservation laws in cellular automata is presented and several characterizations of them are summarized. Computational problems regarding cons...

By exploiting the mathematical analogy between the propagation of sound in a nonhomogeneous potential flow and the propagation of a scalar field in curved space-time, various wave "energy" and wave "momentum" conservation laws are established in a systematic manner. In particular, the acoustic energy conservation law due to Blokhintsev appears as the result of the conservation of a mixed covari...

In this paper we formulate a number of teaching paradoxical problems, dealing with the energy–momentum conservation law in a bound electromagnetic field.

We show that radially symmetric spikes are unstable in a class of reaction-diffusion equations coupled to a conservation law. 1

An exact solution of Lorentz-Dirac equations where the energy conservation law is violated, is described herein for the case of two charges.

We establish a necessary and sufficient condition for decay of periodic entropy solutions to a multidimensional conservation law with merely continuous flux vector.

By a conservation law we mean a quantity constructed from the coordinates, velocities, accelerations, etc. of the system that does not change as the system evolves in time. When the equations of motion are second order, conservation laws typically arise as functions on the velocity phase (possibly with explicit time dependence). Conservation of energy, momentum and angular momentum are familiar...

In [28] Rasin and Hydon suggested a way to construct an infinite number of conservation laws for the discrete KdV equation (dKdV), by repeated application of a certain symmetry to a known conservation law. It was not decided, however, whether the resulting conservation laws were distinct and nontrivial. In this paper we obtain the following results: (1) We give an alternative method to construc...