Exploring symmetry and local conservation laws of generalized fifth order KdV equation

Aim: Many special properties of the evolution equations are derived from their symmetry as well as from their local conservation laws. We now utilize the developing theory of multi-symplecticity to study the inner properties of the generalized fifth order KdV equation. Sections 1 and 2 of the full paper explain our explorative research in some detail. In addition to briefing past research, the core of section 1 is that we derive eq.(9) as the first order symmetric form for the generalized fifth order KdV equation by introducing the momentum series eq.(7). The core of section 2 consists of: (1) we prove that the symmetric form eq.(9) satisfies the multi-symplectic conservation law eq.(10) recurring to the outer product; (2) using the multi-symplectic theory, we derive the local energy conservation law eq.(17) and the local momentum conservation law eq.(19); they express the local properties of the generalized fifth order KdV equation. The results of this paper appear to allow studying the geometric properties of the high order evolution equation in a new way.