An exact nonsingular solitary wave solution of the SchÃ¤ferâ€“Wayne short pulse equation is derived from the breather solution of the sine-Gordon equation by means of a transformation between these twoâ€¦ (More)

We study four distinct second-order nonlinear equations of Rabelo which describe pseudospherical surfaces. By transforming these equations to the constant-characteristic form we relate them to someâ€¦ (More)

The paper contains five examples of using cyclic bases of zero-curvature representations in studies of weak and strong Lax pairs, hierarchies of evolution systems, and recursion operators.

The Hunterâ€“Saxton equation and the Gurevichâ€“Zybin system are considered as two mutually non-equivalent representations of one and the same Whitham-type equation, and all their common solutions areâ€¦ (More)

The gauge-invariant description of zero-curvature representations of evolution equations is applied to the problem of how to distinguish the fake Lax pairs from the true Lax pairs. The mainâ€¦ (More)

The singularity analysis is carried out for a system of four first-order quadratic ODEs with a parameter, which was proposed recently by Golubchik and Sokolov. A transformation of dependent variablesâ€¦ (More)