The General Solution of Coupled Riccati Equations Based on Nonlinear Superposition

Abstract

Due to the fact that the Riccati equations are nonlinear equations, it is difficult to obtain its analytical solution by using commonly used elementary integration methods. We discuss the calculation of general solution for a class of coupled Riccati equations. Firstly, the nonlinear superposition theorem of ordinary differential equations is given; Then the general solution expression and properties of coupled Riccati equations are obtained on the basis of known particular solutions; Finally, a special type of Riccati equations are calculated by the nonlinear superposition formula, which shows that the nonlinear superposition is effective for the integration of nonlinear equations. Nonlinear superposition method has universal significance in constructing new composite exact solutions for nonlinear evolution equations.