Group-Theoretic Approach to the Conservation Laws of KP Equation in Lagrangian and Hamiltonian Formalism

摘要

We have obtained the conservation laws for some nonlinear system through the use of Noether's theorem, Lagrangian theory and Lie symmetry. Though in principle for each generator of Lie symmetry there is a conserved vector yet due to the Lie algebra generated by these generators some of these vectors become linearly dependent. So we have searched for the minimum number of independent conserved vector and have called it a basis of the conservation laws. Such bases of conservation laws are obtained in the case of the KP equation in three dimensions. Next we have shown how the same analysis can be performed in a compact manner through the use of the Hamiltonian formalism. The only difference is that the later methodology yields the time component of the conserved vector and their linear dependence. 7 references, 1 table. (ERA citation 12:029589)