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The (2 + 1)-dimensional fifth-order KdV equation is an important higher-dimensional
and higher-order extension of the famous KdV equation in fluid dynamics. In this
paper, by constructing new test functions, we investigate the periodic solitary
wave solutions for the (2 + 1)-dimensional fifth-order KdV equation by virtue of
the Hirota bilinear form. Several novel analytic solutions for such a model are
obtained and verified with the help of symbolic computation.
(BO) equation is an important nonlinear wave model which can describe the deep
oceanic internal wave propagation. In this paper, the multi-algebraic solitary
wave solutions for the internal wave BO equation including the linear velocity
term in matrix form are given by the bilinear form. Based on the analytic
solutions of the BO equation obtained in this paper and considering the
hydrological parameters, the propagation of one-solitary wave and different
kinds of interaction for the two-solitary waves are discussed and illustrated.