Special symmetries to standard Riccati equations and applications (Q984342)

The general Riccati equation \[ \frac{d\phi(\xi)}{d\xi}=p(\xi)\phi^2(\xi)+q(\xi)\phi(\xi)+r(\xi) \tag{1} \] is studied. Here, \(p,q\) and \(r\) are continuous functions, defined on some interval \([a,b]\subseteq\mathbb{R}\). Using Lie group symmetry, the authors obtain new integrability conditions for the generalized Riccati equation. Using this condition, 7 families of Riccati equations in standard form (1) are obtained which are integrable by quadratures. The obtained results are applied to construct travelling wave solutions for nonlinear evolution equations.