
Journal of Lie Theory 23 (2013), No. 4, 921935 Copyright Heldermann Verlag 2013 On the Isospectral Sixth Order SturmLiouville Equation Kazem Ghanbari Mathematics Department, Sahand University of Technology, Tabriz, Iran kghanbari@sut.ac.ir Hanif Mirzaei Mathematics Department, Sahand University of Technology, Tabriz, Iran h.mirzaei@sut.ac.ir We investigate families of sixthorder SturmLiouville equations having the same spectrum. We factorize the SturmLiouville operator as the product of a third order linear differential operator and its adjoint. By reversing the order of the factors we obtain another sixthorder SturmLiouville operator which is isospectral with the initial operator. The factorization is possible provided the coefficients of the factors satisfy a system of nonlinear thirdorder ordinary differential equations so called principal system. The coefficients in the factorization products are solutions of the principal system. We study this system by using Lie group of symmetries and we show that it may admit a one or two parameter Lie group of transformations. One of the cases leads to Chazy's equation which admits a three parameter Lie group of transformations. In some cases, we solve the system and obtain an isospectral operator. Keywords: Sixth order SturmLiouville equation, isospectral, Lie group symmetries. MSC: 34B24, 70G65 [ Fulltextpdf (284 KB)] for subscribers only. 