A Kirchhoff equation with infinite conservation laws

Abstract

We show here that the quasilinear Kirchhoff-Pokhozhaev equation $$u_{tt}-(a{\int }_{{\mathbb{R}}^n}|\nabla u{|}^{2}dx+b{)}^{-2}\hat{I}”u=0,$$ with $a\ne 0$, admits conservation laws of all orders.