Research paperLie symmetry analysis of the Heisenberg equation

- We perform the Lie symmetry analysis on the Heisenberg equation from the statistical physics.
- Lie point symmetries and optimal system of one-dimensional subalgebras are determined.
- The similarity reductions and exact solutions are obtained.
- Using the multipliers, some conservation laws are obtained.
- The conservation laws associated with symmetries of this equation are constructed by means of Ibragimov's method.

The Lie symmetry analysis is performed on the Heisenberg equation from the statistical physics. Its Lie point symmetries and optimal system of one-dimensional subalgebras are determined. The similarity reductions and invariant solutions are obtained. Using the multipliers, some conservation laws are obtained. We prove that this equation is nonlinearly self-adjoint. The conservation laws associated with symmetries of this equation are constructed by means of Ibragimov's method.