On the well-posedness of the exp-Rabelo equation

Abstract

The exp-Rabelo equation describes pseudo-spherical surfaces. It is a nonlinear evolution equation. In this paper, the well-posedness of bounded from above solutions for the initial value problem associated with this equation is studied.

A note on the non-homogeneous initial boundary problem for an Ostrovsky-Hunter type equation

“…It was introduced both Kozlov and Sazonov [23] as a model equation describing the nonlinear propagation of optical pulses of a few oscillations duration in dielectric media, and Schäfer and and Wayne [37] as a model equation describing the propagation of ultra-short light pulses in silica optical fibers. Moreover, [2,5,36,34] show that (16) is a particular Rabelo equation which describes pseudospherical surfaces. It also is interesting to remind that equation (16) was proposed earlier in [29] in the context of plasma physic and that the similar equations describe the dynamics of radiating gases [25,39].…”

On the initial-boundary value problem for a non-local elliptic-hyperbolic system related to the short pulse equation

“…In [3,4,30,[63][64][65], the authors show that (1.5) is also a non-slowly-varying envelope approximation model that describes the physics of few-cycle-pulse optical solitons. Meanwhile, [5,24,72,74] show that (1.5) is a particular Rabelo equation which describes pseudospherical surfaces.…”

On classical solutions for the fifth‐order short pulse equation

“…In several studies, 5–10 the authors prove that () is also a nonslowly varying envelope approximation model that describes the physics of few‐cycle‐pulse optical solitons. Moreover, several studies 11–14 show that () is a particular Rabelo equation, which describes pseudospherical surfaces.…”