Higher-order corrections to the short-pulse equation

Using renormalization group techniques, we derive an extended short-pulse equation as an approximation to a nonlinear wave equation. We investigate the new equation numerically and show that the new equation captures efficiently higher-order effects on pulse propagation in cubic nonlinear media. We illustrate our findings using one-and two-soliton solutions of the first-order short-pulse equation as initial conditions in the nonlinear wave equation.