A Novikov equation describing pseudo-spherical surfaces, its pseudo-potentials, and local isometric immersions

We show that an equation discovered in V. Novikov [Generalizations of the Camassa-Holm equation, J Phys A: Math Theor. 2009; 42: paper 342002] describes pseudo-spherical surfaces and is geometrically integrable. From the geometric structure of the equation we obtain an infinite hierarchy of conservation laws. The problem of local isometric immersions is also considered.

Automated summary

This study demonstrates that an equation discovered by V. Novikov describes pseudo-spherical surfaces and is geometrically integrable, resulting in an infinite hierarchy of conservation laws. The problem of local isometric immersions is also examined in the context of this equation.