Group-theoretic approach to the conservation laws of the KP equation in Lagrangian and Hamiltonian formalism (Q1100643)

The conservation laws - precisely speaking, the basis of the conservation laws - are obtained through the use of Noether's theorem, Lie symmetry, and a theorem due to Ibragimov. Though in principle for each generator of Lie symmetry there should be a different conserved vector, due to the closed Lie algebra generated by the generators, some of these vectors become no longer independent. The theorem of Ibragimov is used to construct a basis in the case of the KP equation in three dimensions. It is then shown how the same analysis can be performed through the Hamiltonian formalism.