Abstract
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.
Highlights
The soliton equations play a very important role in the study of nonlinear phenomena in different fields such as the fluid physics, nonlinear optics, plasma physics and so on [1] [2]
Dai has presented that the periodic solitary wave solutions for the soliton equations can be obtained by suitable test functions using the bilinear form [8]
As the important (2 + 1)-dimensional higher-order generalization of the KdV equation, the solutions for the (2 + 1)-dimensional fifth-order KdV equation are good at understanding the nonlinear phenomena in the fluid dynamics
Summary
The soliton equations play a very important role in the study of nonlinear phenomena in different fields such as the fluid physics, nonlinear optics, plasma physics and so on [1] [2]. With the development of soliton theory, there are many systematic approaches solving different kinds of soliton solutions, such as the inverse scattering transformation [1] [2], the Darboux transformation [3], the variable seperation method [4], the bilinear method and so on [5]-[7] Among those methods, the bilinear method is a powerful and direct approach to find soliton solutions for the nonlinear partial differential equations. Dai has presented that the periodic solitary wave solutions for the soliton equations can be obtained by suitable test functions using the bilinear form [8]. (2014) The Periodic Solitary Solutions for the (2 + 1)-Dimensional Fifth-Order KdV Equation. With the help of symbolic computation, some novel periodic solitary wave solutions for Equation (1) will be derived based on the bilinear form
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