Abstract:
Several nonlinear phenomena in physics, modelled by the nonlinear differential
equations, can describe also the evolution of surfaces in time. The interaction
between differential geometry of surfaces and nonlinear differential equations has
been studied since the 19th century. This relationship is based on the fact that
most of the local properties of surfaces are expressed in terms of nonlinear dif
ferential equations. Since the famous sine-Gordon and Liouville equations, the
interrelation between nonlinear differential equations of the classical differential
geometry of surfaces and modern soliton equations has been studied from vari
ous points of view in numerous papers. In particular, the relationship between
deformations of surfaces and integrable systems in 2+1 dimensions was studied
by several authors.
