We use an inverse scattering approach to study multi-peakon solutions of the Degasperis–Procesi (DP) equation, an integrable PDE similar to the Camassa–Holm shallow water equation. The spectral problem associated to the DP equation is equivalent under a change of variables to what we call the cubic string problem, which is a third order non-selfadjoint generalization of the well-known equation ...

Cubic Hermite interpolation ensures continuity of derivatives between elements, so as well as providing an excellent representation of a smooth function, it also accurately models its gradients. Another attractive feature of this interpolation is that because each node is shared by neighbouring elements, a mesh of cubic Hermite elements has no more unknowns than a mesh of quadratic Lagrange ele...

A quintic nonlinear Schrödinger (NLS) equation, with derivative cubic terms, that governs the propagation of nonlinear signals in a nonlinear transmission line (NLTL) is considered. By combining a special phase-imprint transformation with a modified lens transformation, we reduce the equation under consideration to a standard cubic NLS equation with a time-varying gain/loss term and obtain the ...

This article discusses cubic curves, some of the ways they arise, and some of their applications in diverse fields such as cryptography and string theory. Key-Words: cubic curve, elliptic curve, Weierstrass equation

We present a convention (for square/cubic root) which provides correct interpretations of Lagrange’s formula for all cubic polynomial equations with real coefficients. Using this convention, we also present a real solution formulas for the general cubic equation with real coefficients under equality and inequality constraints.