Lagrange solution for three wavelength solitary wave clusters in nematic liquid crystals

► Modulation solutions for three interacting solitary waves of three different wave-lengths (colours) in a nematic liquid crystal, so-called nematicons, are derived. ► Equations for positions of nematicons analogous to equations for gravitating masses. ► Solutions are analogous to the Lagrange triangle solution of Newtonian mechanics. ► Nematicon triangle solutions not an equilateral triangle due to form of potential. ► Triangle configuration shown to be stable to diffractive radiation losses.