Breakdown of pseudospherical surfaces determined by the Camassa-Holm equation (Q6065745)

The Camassa-Holm equation is a shallow water model, which plays an important role in mathematical physics. The paper is concerned with connections between the Camassa-Holm equation and pseudospherical surfaces. The author considers the relations between Cauchy problems involving the Camassa-Holm equation and the intrinsic geometry associated to the corresponding solutions, and shows that any Cauchy problem involving an initial datum gives rise the a pseudospherical surface. The author also shows that singularities of the solutions are inherited by the corresponding first fundamental forms, and he precisely describes two blow up scenarios of the surfaces.