Archilla, J. F. R.; Romero, J. L.; Romero Romero, F.; Palmero, F. Lie symmetries and multiple solutions in \(\lambda-\omega\) reaction-diffusion systems. (English) Zbl 0924.35061 J. Phys. A, Math. Gen. 30, No. 1, 185-194 (1997). The \(\lambda - \omega\) reaction-diffusion system of the form \[ u_t=D\nabla^2u+\lambda (z)u-\omega (z)v,\qquad v_t=D\nabla^2v+\omega (z)u+\lambda (z)v \] is considered, where \(u=u(x,y,t)\), \(v=v(x,y,t)\), \(D\) is a constant, \(z=(u^2+v^2)^{1/2}\), \(\lambda (z)\) is a positive function of \(z\) for \(0\leq z< z_0\) and negative for \(z>z_0\), \(\omega (z)\) is a positive function. The symmetry algebra generated by translations with respect to \(x, y, t\), rotations in the plane \((x,y)\) and rotations in the plane \((u,v)\) is considered. Invariant solutions with respect to different subalgebras of this algebra are obtained. Reviewer: V.A.Yumaguzhin (Pereslavl’-Zalesskij) Cited in 3 Documents MSC: 35K57 Reaction-diffusion equations 58J70 Invariance and symmetry properties for PDEs on manifolds 35K40 Second-order parabolic systems Keywords:classical symmetry; invariant solution PDFBibTeX XMLCite \textit{J. F. R. Archilla} et al., J. Phys. A, Math. Gen. 30, No. 1, 185--194 (1997; Zbl 0924.35061) Full Text: DOI Link