Nonclassical approximate symmetries of evolution equations with a small parameter (Q2495194)

The author indicates that the method developed in this paper can be applied to a large class of PDEs with a small parameter, not only to the evolution ones. The author considers \[ u_t=uu_x+\varepsilon H(t,x,u, u_x,u_{xx},\dots).\tag{1} \] She considers (1) as perturbations of the transport equation \(u_t=uu_x\) and constructs approximate nonclassical symmetries of these equations, starting from exact nonclassical symmetries of the transport equation. Using these approximate nonclassical symmetries and the reduction theorem, the author finds approximate conditionally invariant solutions of the equations under consideration.