Silindir, Burcu2023-06-162023-06-1620121687-1847https://doi.org/10.1186/1687-1847-2012-121https://hdl.handle.net/20.500.14365/2256This 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.eninfo:eu-repo/semantics/openAccessHirota direct methodq-Toda latticeq-soliton solutionsq-exponential identityq-Hirota D-operatorDe-Vries EquationMultiple CollisionsArticle10.1186/1687-1847-2012-1212-s2.0-84871321859