Tomasz Czyżycki
Nonlinear superposition principle for Riccati equation
It is well known that linear combination of solutions represent a new solution of a linear system of algebraic equations as well as differential or difference ones. For nonlinear equations it is not true but in some cases we can find nonlinear principle of superposition, it means nonlinear formula which allows to compose some known solutions and obtain a new solution. In this talk we present examples of such principle, especially for scalar Riccati equation in general form, connections with group theory and applications in mathematical physics problems.
