Abstract
I study the geometric notion of a differential system describing surfaces of a constant negative curvature and describe a family of pseudospherical surfaces for the nonlinear partial differential equations with constant Gaussian curvature <svg style="vertical-align:-0.0pt;width:18.262501px;" id="M1" height="10.9125" version="1.1" viewBox="0 0 18.262501 10.9125" width="18.262501" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(.017,0,0,-.017,.062,10.863)"><path id="x2212" d="M535 230h-483v50h483v-50z"/></g><g transform="matrix(.017,0,0,-.017,10.041,10.863)"><path id="x31" d="M384 0h-275v27q67 5 81.5 18.5t14.5 68.5v385q0 38 -7.5 47.5t-40.5 10.5l-48 2v24q85 15 178 52v-521q0 -55 14.5 -68.5t82.5 -18.5v-27z"/></g> </svg>.
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