Reformulation of Degasperis-Procesi Field by Functional Derivatives

Abstract

We reformulated the Degasperis-Procesi equation using functional derivatives. More specifically, we used a semi-inverse method to derive the Lagrangian of the Degasperis-Procesi equation. After introducing the Hamiltonian formulation using functional derivatives, we applied this new formulation to the Degasperis-Procesi Equation. In addition, we found that both Euler-Lagrange equation and Hamiltonian equation yield the same result. Finally, we studied an example to elucidate the results.

Keywords: Functional derivatives, Hamiltonian systems, Degasperis-Procesi equation, Euler-Lagrange.