We develop the method for constructing Lax representations of pde s via twisted extensions of their algebras of contact symmetries by generalizing the construction to Lie–Rinehart algebras. We present examples of application of the proposed technique.

. We ﬁnd new integrable partial diﬀerential equations with Lax representations generated by extensions of Lie algebras of the Kac–Moody type as well as the Lie algebra of Hamiltonian vector ﬁelds on… Expand

Equations of dispersionless Hirota type $$\begin{aligned} F(u_{x_ix_j})=0 \end{aligned}$$ F ( u x i x j ) = 0 have been thoroughly investigated in mathematical physics and differential geometry. It… Expand