Tzitzeica equation

The Tzitzeica equation is a nonlinear partial differential equation devised by Gheorghe Țițeica in 1907 in the study of differential geometry, describing surfaces of constant affine curvature.

[1] The Tzitzeica equation has also been used in nonlinear physics, being an integrable 1+1 dimensional Lorentz invariant system.

= exp ⁡ ( u ) − exp ⁡ ( − 2 u ) .

On substituting the equation becomes

One obtains the traveling solution of the original equation by the reverse transformation