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math-ph2026
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…
math-ph2026
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…