Solitary wave interactions for the modified equal width equation (Q1568595)

The numerical solution of the modified equal width equation in one space dimension, \[ u_t-\mu u_{xxt}+ 3u^2 u_x= 0,\quad \mu> 0, \] is considered. The exact solutions in an infinite domain with \(u\to 0\) as \(x\to\pm\infty\) are solitary waves having the same width. Moreover, they fulfill some invariant principles. The spatial discretization is a collocation method using quintic B-splines and equidistant nodal points. For the temporal discretization, the Crank-Nicolson scheme is applied. The linearized method is shown to be unconditionally stable in the sense of von Neumann. The author studies three different test cases: the motion of a single solitary wave that fulfills the invariance principles, the inelastic interaction of two solitary waves, and the birth of a soliton from the initial condition.