21 citations · 28 across the 5 of their papers we have counts for
6 papers
A look on equations describing pseudospherical surfaces
Igor Leite Freire
We revisit the notion of equations describing pseudospherical surfaces, starting from the works by Sasaki, whose roots were influenced by the AKNS system, the works by Chern and Te…
Global and blow-up solutions for a non-local integrable equation with applications to geometry
Nilay Duruk Mutlubas, Igor Leite Freire
We establish the global existence of higher-order Sobolev solutions for a non-local integrable evolution equation arising in the study of pseudospherical surfaces and non-linear wa…
Local isometric immersions and breakdown of manifolds determined by Cauchy problems of the Degasperis-Procesi equation
Igor Leite Freire
We prove that both local and non-local formulations of the Degasperis-Procesi equation possess a pseudospherical nature. As a result, solutions determined by Cauchy problems with n…
Intrinsic geometry and wave-breaking phenomena in solutions of the Camassa-Holm equation
Igor Leite Freire
Pseudospherical surfaces determined by Cauchy problems involving the Camassa-Holm equation are considered herein. We study how global solutions influence the corresponding surface,…
Existence and uniqueness of periodic pseudospherical surfaces emanating from Cauchy problems
Nilay Duruk Mutlubas, Igor Leite Freire
We study implications and consequences of well-posed solutions of Cauchy problems of a Novikov equation describing pseudospherical surfaces. We show that if the co-frame of dual on…
Conserved quantities, continuation and compactly supported solutions of some shallow water models
Igor Leite Freire
A proof that strong solutions of the Dullin-Gottwald-Holm equation vanishing on an open set of the (1+1) space-time are identically zero is presented. In order to do it, we use a g…