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Potential symmetries and direct reduction methods of order two. (English) Zbl 0932.35009
It is proved that for any PDE written in the conservative form \[ D_xF(x,t,u,u_t,u_x)-D_tG(x,t,u,u_t,u_x)=0, \] any compatible differential constraint of second order defines a non-classical potential symmetry.

MSC:
35A30 Geometric theory, characteristics, transformations in context of PDEs
35C05 Solutions to PDEs in closed form
35Q40 PDEs in connection with quantum mechanics
58J70 Invariance and symmetry properties for PDEs on manifolds
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