Applied Physics and Mathematics Annotation << Back Quantitative indicators of solutions of Diophantine equations and systems in the domain of natural numbers V.L. Vol'fson The paper shows that the asymptotic density of solutions of Diophantine equations or systems of the natural numbers is 0. The author gives the methods and studied estimates of the number, density and probability k-tuples to be the solution of algebraic equations for the first, second and higher orders of two or more variables, non-algebraic Diophantine equations and systems of Diophantine equations in the domain of natural numbers. The paper contains the geometric proof of the estimate the number of solutions of Diophantine equations for two, three or more variables in the natural numbers. The author proves the assertion about the number of solutions of algebraic Diophantine equations of higher orders in the domain of natural numbers. The author provides estimates for the asymptotic behavior of quantitative solutions of Diophantine equations and systems in the domain of natural numbers. Keywords: Diophantine equation, algebraic equation, the order of an algebraic equation, a non-algebraic equation, system, the number of solutions, the domain of natural numbers, the asymptotic density of the solutions, the probability, k-tuples. Contacts: E-mail: znakvicvolf@mail.ru Pp. 50-64.