In a river or an ocean: Similarity-reduction work on a (3+1)-dimensional extended shallow water wave equation

Abstract

Researchers have recently become interested in a (3+1)-dimensional extended shallow water wave equation in a river or an ocean. This equation could be used to represent a variety of the physical phenomena that have some impacts on the environment, such as the floods and tsunamis. Two sets of the similarity reductions are discovered for that equation based on the variable coefficients, connected with the potential applications of the equation in a river or an ocean.