Soliton solutions of q-Toda lattice by Hirota direct method

Silindir B.

ADVANCES IN DIFFERENCE EQUATIONS, 2012 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Basım Tarihi: 2012
  • Doi Numarası: 10.1186/1687-1847-2012-121
  • Dergi Adı: ADVANCES IN DIFFERENCE EQUATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Anahtar Kelimeler: Hirota direct method, q-Toda lattice, q-soliton solutions, q-exponential identity, q-Hirota D-operator, DE-VRIES EQUATION, MULTIPLE COLLISIONS
  • Dokuz Eylül Üniversitesi Adresli: Hayır

Özet

This paper presents the q-analogue of Toda lattice system of difference equations by discussing the q-discretization in three aspects: differential-q-difference, q-difference-q-difference and q-differential-q-difference Toda equation. The paper develops three-q-soliton solutions, which are expressed in the form of a polynomial in power functions, for the differential-q-difference and q-difference-q-difference Toda equations by Hirota direct method. Furthermore, it introduces q-Hirota D-operator and presents the q-differential-q-difference version of Toda equation. Finally, the paper presents its solitary wave like a solution in terms of q-exponential function and explains the nonexistence of further solutions in terms of q-exponentials by the virtue of Hirota perturbation.