Application of new triangular functions to nonlinear partial differential equations

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Abdel-Salam E. A., KAYA D.

Zeitschrift fur Naturforschung - Section A Journal of Physical Sciences, cilt.64, sa.1-2, ss.1-7, 2009 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 64 Sayı: 1-2
  • Basım Tarihi: 2009
  • Doi Numarası: 10.1515/zna-2009-1-201
  • Dergi Adı: Zeitschrift fur Naturforschung - Section A Journal of Physical Sciences
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1-7
  • Anahtar Kelimeler: Exact solutions, Nonlinear evolution equations, Traveling wave solutions, Triangular fibonacci functions
  • İstanbul Ticaret Üniversitesi Adresli: Evet

Özet

The results of some new research on a new class of triangular functions that unite the characteristics of the classical triangular functions are presented. Taking into consideration the great role played by triangular functions in geometry and physics, it is possible to expect that the new theory of the triangular functions will bring new results and interpretations in mathematics, biology, physics and cosmology. New traveling wave solutions of some nonlinear partial differential equations are obtained in a unified way. The main idea of this method is to express the solutions of these equations as a polynomial in the solution of the Riccati equation that satisfy the symmetrical triangular Fibonacci functions. We apply this method to the combined Korteweg-de Vries (KdV) and modified KdV (mKdV) equations, the generalized Kawahara equation, Ito's 5th-order mKdV equation and Ito's 7th-order mKdV equation. © 2009 Verlag der Zeitschrift für Naturforschung.