7 papers
A Rigorous Proof of Metric Blow-Up for Pseudospherical Metrics Associated with the Degasperis--Procesi Equation
Zhenhua Shi, Mingyue Guo
This paper studies finite-time blow-up of pseudospherical metrics induced by solutions of the Cauchy problem for the Degasperis--Procesi equation. For initial momentum profiles sat…
Systems of partial differential equations describing pseudo-spherical or spherical surfaces
Mingyue Guo, Jing Kang, Zhenhua Shi
In this paper, we study systems of nonlinear partial differential equations which describe surfaces of constant curvature. From the flatness condition of connection 1-forms, we pre…
On a class of third order differential equations describing pseudospherical or spherical surfaces
Mingyue Guo, Jing Kang, Zhenhua Shi +1
In this paper, we study third order nonlinear partial differential equations which describe surfaces of constant curvature. From the flatness of connection 1-forms, we present a cl…
Local isometric immersions of pseudospherical surfaces described by a class of third order differential equations
Mingyue Guo, Zhenhua Shi
We discuss a specific type of pseudospherical surfaces defined by a class of third order differential equations, of the form , an…
Local isometric immersions of pseudospherical surfaces described by a class of third order partial differential equations
Mingyue Guo, Zhenhua Shi
In this paper, we study the problem of local isometric immersion of pseudospherical surfaces determined by the solutions of a class of third order nonlinear partial differential eq…
Pseudo-potentials and local isometric immersion for a generalized Camassa-Holm equation describing pseudospherical surfaces
Mingyue Guo, Zhenhua Shi
A generalized Camassa-Holm equation, which describes pseudospherical surfaces, is considered. Using geometric methods, it is demonstrated that the equation is geometrically integra…