The nonclassical symmetries method is applied to a class of reaction-diffusion equations with nonlinear source, i.e. ut=uxx+cux+R(u, x). Several cases are obtained by using suitable solutions the heir-equations as described in [M.C. Nucci, Nonclassical special heir-equations, J. Math. Anal. Appl. 279 (2003) 168–179].

We theoretically study the emission statistics of a weakly nonlinear photonic dimer during coherent oscillations. We show that the phase and population dynamics allow to periodically meet an optimal squeezing condition resulting in a strongly nonclassical emission statistics. By considering an exciton-polariton Josephson junction driven resonantly by a pulsed classical source, we show that a si...

We consider the Riemann problem for non-genuinely nonlinear conservation laws where the flux function admits two inflection points. This is a simplification of van der Waals fluid pressure, which can be seen as a function of the specific volume for a specific entropy at which the system lacks the non-genuine nonlinearity. Corresponding to each inflection point, A nonclassical Riemann solver can...

Many secreted polypeptide regulators of angiogenesis are devoid of signal peptides. These proteins are released through nonclassical pathways independent of endoplasmic reticulum and Golgi. In most cases, the nonclassical protein export is induced by stress. It usually serves to stimulate repair or inflammation in damaged tissues. We review the secreted signal peptide-less regulators of angioge...