Max-plus equation with two conserved quantities and one monotonically decreasing quantity

抄録

We propose a max-plus equation as an extension of $1+1$D cellular automaton of four neighbors. It has two conserved quantities and one monotonically decreasing quantity which are max-plus analogues of those of the binary cellular automaton. It is interesting that one of the quantities is global and defined by the maximum value of dependent variable. We show proofs about their conservation and monotonicity using max-plus formulas.