On nonlinear partial differential equations with an infinite-dimensional conditional symmetry

@misc{citeulike:2805385, abstract = {The invariance of nonlinear partial differential equations under a certain infinite-dimensional Lie algebra A\_N(z) in N spatial dimensions is studied. The special case A\_1(2) was introduced in J. Stat. Phys. {\bf 75}, 1023 (1994) and contains the Schr\"odinger Lie algebra sch\_1 as a Lie subalgebra. It is shown that there is no second-order equation which is invariant under the massless realizations of A\_N(z). However, a large class of strongly non-linear partial differential equations is found which are conditionally invariant with respect to the massless realization of A\_N(z) such that the well-known Monge-Ampere equation is the required additional condition. New exact solutions are found for some representatives of this class.}, author = {Cherniha, Roman and Henkel, Malte }, citeulike-article-id = {2805385}, eprint = {math-ph/0402059}, keywords = {cosmo, mak, transport}, month = {Oct}, posted-at = {2008-05-16 15:35:12}, priority = {2}, title = {On nonlinear partial differential equations with an infinite-dimensional conditional symmetry}, url = {http://arxiv.org/abs/math-ph/0402059}, year = {2004} }

TY - ELEC ID - citeulike:2805385 L3 - citeulike-article-id:2805385 TI - On nonlinear partial differential equations with an infinite-dimensional conditional symmetry N2 - The invariance of nonlinear partial differential equations under a certain infinite-dimensional Lie algebra A_N(z) in N spatial dimensions is studied. The special case A_1(2) was introduced in J. Stat. Phys. {\bf 75}, 1023 (1994) and contains the Schr\"odinger Lie algebra sch_1 as a Lie subalgebra. It is shown that there is no second-order equation which is invariant under the massless realizations of A_N(z). However, a large class of strongly non-linear partial differential equations is found which are conditionally invariant with respect to the massless realization of A_N(z) such that the well-known Monge-Ampere equation is the required additional condition. New exact solutions are found for some representatives of this class. KW - cosmo KW - mak KW - transport AU - Cherniha, Roman AU - Henkel, Malte PY - 2004/Oct/08/ UR - http://arxiv.org/abs/math-ph/0402059 ER -