Fifth-order evolution equations describing pseudospherical surfaces

Smoothing of a Class of Fifth Order Model Evolution Equations

Solutions of a class of fth-order model evolution equations corresponding to initial data in relatively weak function spaces are shown to exhibit a smoothing eeect of the type of Kato. These models include the next hierarchy of the Korteweg-de Vries equation. It is interesting to observe that conditions that guarantee smoother solutions in some of these weaker function spaces are exactly the on...

Pseudospherical surfaces on time scales

We define and discuss the notion of pseudospherical surfaces in asymptotic coordinates on time scales. Two special cases, namely dicrete pseudospherical surfaces and smooth pseudosperical surfaces are consistent with this description. In particular, we define the Gaussian curvature in the discrete case. Mathematics Subject Classification 2000: 53A05, 39A12, 52C07, 65D17. PACS Numbers: 02.40.Hw,...

Localized Induction Equation and Pseudospherical Surfaces

We describe a close connection between the localized induction equation hierarchy of integrable evolution equations on space curves, and surfaces of constant negative Gauss curvature. To appear in Journal of Physics A: Mathematical and General PACS numbers: 03.40.Gc, 02.40.+m, 11.10.Lm, 68.10-m 2 RON PERLINE

Travelling Wave Solutions for the KdV-Burgers-Kuramoto and Nonlinear Schrödinger Equations Which Describe Pseudospherical Surfaces

Fifth-Order Weighted Power-ENO Schemes for Hamilton-Jacobi Equations

We design a class of Weighted Power-ENO (Essentially Non-Oscillatory) schemes to approximate the viscosity solutions of Hamilton-Jacobi (HJ) equations. The essential idea of the Power-ENO scheme is to use a class of extended limiters to replace the minmod type limiters in the classical third-order ENO schemes so as to improve resolution near kinks where the solution has discontinuous gradients....