Chebyshev–Chebyshev spectral collocation method for solving the generalized regularized long wave (GRLW) equation

In this research, a Chebyshev–Chebyshev spectral collocation method based on Kronecker and Hadamard products is proposed for solving the generalized regularized long wave (GRLW) equation. Chebyshev–Gauss–Lobatto collocation points are used in both time and space directions. Three invariants of motion: mass, momentum and energy are evaluated to determine the conservation properties of the GRLW equation. The single solitary wave and the interaction of two and three solitary waves are presented to validate the efficiency and the accuracy of the proposed scheme.