This monograph is planned to provide the application of the soliton theory to solve certain
practical problems selected from the fields of solid mechanics, fluid mechanics and …

In this study, the conditions of a regular curve to be Tzitzeica curve according to Type‐1 and
Type‐2 Bishop frames in Euclidean 3‐space are formulated. Also, the conditions for each …

In this study, we consider Tzitzeica curves (Tz-curves) in a Euclidean 3-space E-3. We
characterize such curves according to their curvatures. We show that there is no Tz-curve …

The determinants of bordered Hessian matrices (also called Allen's matrices) play important
roles in many areas of mathematics and economics. In the present paper, we completely …

The aim of this paper is to present a generalization of the Tzitzeica curve equation based on
a new centro-affine invariant. The third order nonlinear ordinary differential equation of the …

On the elliptic cylindrical Tzitzeica curves in Minkowski 3-space Page 50 Scientia Magna Vol. 5
(2009), No. 3, 44–48 On the Elliptic cylindrical Tzitzeica curves in Minkowski 3-Space Murat …

The Tzitzeica curve equation is a nonlinear ordinary differential equation arising in
differential geometry whose solutions define a space curve for which the ratio of its torsion …

In this paper we study the ruled surfaces generated by elliptic cylindrical curves in the
isotropic 3-space 𝕀 3. We classify such surfaces in 𝕀 3 with constant curvature and …

The purpose of the paper is to analyze the Tzitzeica curve equation from the point of view of
symmetry analysis theory. The Tzitzeica curve equation is a nonlinear ordinary differential …

Gheorghe Tzitzeica who is a Romanian mathematician (1873-1939) introduced a class of
curves, nowadays called Tzitzeica curves and a class of surfaces of the Euclidean 3-space …