Abstract
In this paper, by means of the Hirota bilinear method, a dimensionally reduced nonlinear evolution equation is investigated. Through its bilinear form, lump solutions are obtained. We construct interaction solutions between lump solutions and one soliton solution by choosing quadratic functions and exponential function. Interaction solutions with the combinations of exponential functions and sine function are also given. Meanwhile, the figures of these solutions are plotted. The dynamical characteristics and properties of obtained solutions are discussed, respectively. The results show that the corresponding physical quantities and properties of nonlinear waves are associated with the values of the parameters.
Highlights
Nonlinear evolution equations (NLEEs) are becoming more and more important in modern science
Lump Solutions Consisting of Two Quadratic Functions
Lump Solutions Consisting of ree Quadratic Functions
Summary
Nonlinear evolution equations (NLEEs) are becoming more and more important in modern science. In order to obtain the solutions of NLEEs, researchers have put forward many methods, including the Hirota direct method [1], Painleveanalysis method [2], inverse scattering transformation (IST) [3, 4], Riemann–Hilbert method [5,6,7], Lie symmetry method, and so on [8,9,10,11,12]. Equation (2) has wide applications in different areas, for example, mathematical physics, ocean science, engineering, and others It could describe propagation of shallow water wave in nonlinear dispersive channel.
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