On the preservation of invariants in the simulation of solitary waves in some nonlinear dispersive equations

In this paper we generalize some results in the literature concerning the structure of numerical approximations to solitary wave solutions of some nonlinear, dispersive equations is studied. We prove that those time discretizations with the property of preserving, exactly or approximately up to certain order, some invariants of the problems, have a better propagation of the error and provide a more suitable simulation of the solitary waves. The generalization involves the treatment of nonlocal operators and two different kinds of equations.

► We study the time behaviour of approximations to solitary waves. ► We generalize previous results to more general nonlinear dispersive equations. ► The analysis includes nonlocal operators and more general nonlinear terms. ► This generalization requires more technical study of the proofs.