A direct rational exponential scheme is offered to construct exact multi-soliton solutions of nonlinear partial differential equation. We have considered the Calogero–Bogoyavlenskii–Schiff equation and KdV equation as two concrete examples to show efficiency of the method. As a result, one wave, two wave and three wave soliton solutions are obtained. Corresponding potential energy of the solito...

T-algebra is an interactive learning environment for step-by-step solving of algebra problems in four areas of mathematics, including linear equations. To make the diagnosis of mistakes more complete and the program more intelligent we designed our own rule dialogue. Each solution step in T-algebra consists of three stages: selection of the transformation rule, marking the parts of expression, ...

Differential-algebraic equations (DAEs) naturally arise in many applications, but present numerical and analytical difficulties. The index of a DAE is a measure of the degree of numerical difficulty. In general, the higher the index is, the more difficult it is to solve the DAE. Therefore, it is desirable to transform the original DAE into an equivalent DAE with lower index. In this paper, we p...