Towards the classification of scalar nonpolynomial evolution equations: Quasilinearity


Bilge A.

COMPUTERS & MATHEMATICS WITH APPLICATIONS, vol.49, pp.1837-1848, 2005 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 49
  • Publication Date: 2005
  • Doi Number: 10.1016/j.camwa.2004.09.014
  • Title of Journal : COMPUTERS & MATHEMATICS WITH APPLICATIONS
  • Page Numbers: pp.1837-1848

Abstract

We prove that, for m >= 7, scalar evolution equations of the form u(t) = F(x, t, u,..., u(m)) which admit a nontrivial conserved density of order m + 1 are linear in u(m). The existence of such conserved densities is a necessary condition for integrability in the sense of admitting a formal symmetry, hence, integrable scalar evolution equations of order m >= 7, admitting nontrivial conserved densities are quasilinear. (c) 2005 Elsevier Ltd. All rights reserved.