Numerical solution for a general class of nonlocal nonlinear wave equations arising in elasticity

Source abstract

Abstract A class of nonlocal nonlinear wave equation arises from the modeling of a one dimensional motion in a nonlinearly, nonlocally elastic medium. The equation involves a kernel function with nonnegative Fourier transform. We discretize the equation by using Fourier spectral method in space and we prove the convergence of the semidiscrete scheme. We then use a fully‐discrete scheme, that couples Fourier pseudo‐spectral method in space and 4th order Runge‐Kutta in time, to observe the effect of the kernel function on solutions. To generate solitary wave solutions numerically, we use the Petviashvili's iteration method.