Nonexistence of local conservation laws for generalized Swift–Hohenberg equation

Abstract

We prove that the generalized Swift-Hohenberg equation with nonlinear right-hand side, a natural generalization of the Swift-Hohenberg equation arising in physics, chemistry and biology and describing inter alia pattern formation, has no nontrivial local conservation laws.

Complete classification of local conservation laws for generalized Cahn–Hilliard–Kuramoto–Sivashinsky equation

“…the discussion in the introduction and in Refs. [15] and [10]. Corollary The generalized Cahn–Hilliard equation (cf.…”

“…Recall that obtaining a complete description of nontrivial local conservation laws for a given PDE, rather than finding a few low‐order ones, is a difficult goal that was achieved only for a rather small number of examples, cf., for example, Refs. [15, 18, 26, 32, 34], and references therein.…”