Abstract. The traditional wave equation models wave propagation in an ideal conducting medium. For characterizing the wave propagation in inhomogeneous media with frequency dependent power-law attenuation, the spacetime fractional wave equation appears; further incorporating the additive white Gaussian noise coming from many natural sources leads to the stochastic spacetime fractional wave equa...

We study the error propagation of time integrators of solitary wave solutions for the regularized long wave equation, ut +ux+ 2 (u)x −uxxt = 0, by using a geometric interpretation of these waves as relative equilibria. We show that the error growth is linear for schemes that preserve invariant quantities of the problem and quadratic for ‘nonconservative’ methods. Numerical experiments are prese...

In this paper, a class of arbitrarily high-order linear momentum-preserving and energy-preserving schemes are proposed, respectively, for solving the regularized long-wave equation. For scheme, key idea is based on extrapolation/prediction-correction technique symplectic Runge-Kutta method in time, together with standard Fourier pseudo-spectral space. We show that scheme linear, high-order, unc...