Symmetry reductions and conservation laws of the short pulse equation

In this letter, we study invariance properties of the nonlinear short pulse equation through Lie symmetry analysis. We show that this leads to several reductions yielding solutions of the short pulse equation. Furthermore, we obtain two conservation laws of the equation through the direct method. We show that two resulting nonlocally related systems yield no nonlocal symmetries of the short pulse equation. Some remarks and appropriate conclusions are drawn at the end.