Towards the classification of scalar nonpolynomial evolution equations: Quasilinearity

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Atıf İçin Kopyala

Bilge A.

COMPUTERS & MATHEMATICS WITH APPLICATIONS, cilt.49, ss.1837-1848, 2005 (SCI-Expanded)

• Yayın Türü: Makale / Tam Makale
• Cilt numarası: 49
• Basım Tarihi: 2005
• Doi Numarası: 10.1016/j.camwa.2004.09.014
• Dergi Adı: COMPUTERS & MATHEMATICS WITH APPLICATIONS
• Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
• Sayfa Sayıları: ss.1837-1848
• İstanbul Teknik Üniversitesi Adresli: Hayır

Özet

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.