On the infinite-dimensional noncommutative Lie–Bäcklund algebra associated with the equations of one-dimensional gas dynamics

A study is made of the infinite-dimensional noncommutative Lie–Bäcklund algebra associated with the equations of one-dimensional plane isentropic flow of a gas and with the infinite set of systems of evolution equations associated with them. Infinite series of invariant solutions and conservation laws and $L-A$ pairs for all these equations are obtained. A new operator method for finding invariant solutions is proposed.