and Applied Analysis 3 Strauss 10 constructed periodic travelling waves with vorticity for the classical inviscid water wave problem under the influence of gravity, described by the Euler equation with a free surface over a flat bottom, and used global bifurcation theory to construct a connected set of such solutions, containing flat waves as well as waves that approach flows with stagnation po...

A spectral solution of the RLW equation based on collocation method using Chebyshev polynomials as a basis for the approximate solution is proposed. Test problems, including the motion of a single solitary wave with different amplitudes are used to validate this algorithm which is found to be more accurate than previous ones. The interaction of solitary waves is used to discuss the effect of th...

1 Aula UTFSM-CIMNE, Departamento de Ingenierı́a Mecánica, Universidad Técnica Federico Santa Marı́a, Avenida España 1680, 2340000 Valparaı́so, Chile 2 Departamento de Matemática, Universidad Técnica Federico Santa Marı́a, Avenida España 1680, 2340000 Valparaı́so, Chile 3 Escuela de Ingenierı́a Mecánica, Pontificia Universidad Católica de Valparaı́so, Los Carrera 01567, Quilpué, 2430120 Valparaı́so, Chile

This paper systematically investigates the Lie group analysis method of time-fractional regularized long-wave (RLW) equation with Riemann–Liouville fractional derivative. The vector fields and similarity reductions are obtained. It is shown that governing can be transformed into a ordinary differential new independent variable, where derivatives in Erdèlyi–Kober sense. Furthermore, explicit ana...