To build accurate solutions to non-linear equations of mathematical physics, a number of methods have been developed based on the transition to new variables (dependent and independent). In this case, the goal is usually set: to find new variables whose number is less than the number of initial ones. Switching to such variables leads to simpler equations. In particular, the search for exact solutions to equations with partial derivatives of two independent variables is reduced to the study of

more »

... dinary differential equations (or systems of such equations). Naturally, with this reduction, solutions of ordinary differential equations do not give all solutions of the original equation with partial derivatives, but only a class of solutions that possess some of their own standards. The simplest classes of exact solutions that describe ordinary differential equations are traveling wave type solutions and auto-model solutions. The existence of these solutions is usually (but not always) due to the invariance of the equations considered with respect to shear and stretch-compression. The phenomenon developing in time is called auto-model, the distribution of its characteristics at different points in time is obtained from another similarity transformation. Auto-modeling allows, in many cases, to reduce the problem of mathematical physics to solving conventional differential equations, which significantly simplifies the study. With the help of auto-model solutions, researchers tried to see the characteristic properties of new phenomena. In addition, automatic solutions were used as benchmarks in evaluating approximate methods for solving more complex tasks. modern computer technology has enabled us to automate solutions to these types of problems complicated. The article describes the use of the method using the example of a self-modal solution in the MAPLE program. We use the above and higher order private equation differential equations when solving university management tasks.