Complete characterization of nontrivial local conservation laws and nonexistence of local Hamiltonian structures for generalized Infeld--Rowlands equation

TL;DR

This paper fully characterizes when a generalized Infeld--Rowlands equation has nontrivial local conservation laws and proves it does not admit local Hamiltonian or symplectic structures, providing a comprehensive understanding of its conservation properties.

Contribution

It provides a complete classification of local conservation laws for the generalized Infeld--Rowlands equation and establishes the nonexistence of local Hamiltonian and symplectic structures.

Findings

All cases with nontrivial local conservation laws are explicitly characterized.

The equation admits no nontrivial local Hamiltonian or symplectic structures.

The methods used can be applied to other PDEs for similar nonexistence results.

Abstract

We characterize all cases when a certain natural generalization of the Infeld--Rowlands equation admits nontrivial local conservation laws of any order, and give explicit form of these conservation laws modulo trivial ones. Furthermore, we prove that the equation under study admits no nontrivial local Hamiltonian and symplectic structures and no nontrivial local Noether and inverse Noether operators; the method of establishing the said nonexistence results can be readily applied to many other PDEs.