Abstract
In this paper, several kinds of lump solutions for the (1 + 1)-dimensional Ito-equation are introduced. The proposed method in this work is based on a Hirota bilinear differential equation. The form of the solutions to the equation is constructed and the solutions are improved through analysis and symbolic computations with Maple. Finally, figure of the solution is made for specific examples for the lump solutions.
Highlights
In recent years, the study to the exact solutions of nonlinear equation is one of the hot topics in nonlinear science
In order to solve the exact solutions of nonlinear partial differential equations (NLPDEs), sciences have come up with lots of ways, for example Backlund transformation [1] [2], Darboux transformation [3] and Hirota bilinear methods [4]
Hirota bilinear forms are one of the integrability characteristics of nonlinear partial differential equations and the bilinear equation can be solved by the Wronskian technique [11]
Summary
The study to the exact solutions of nonlinear equation is one of the hot topics in nonlinear science. In order to solve the exact solutions of NLPDEs, sciences have come up with lots of ways, for example Backlund transformation [1] [2], Darboux transformation [3] and Hirota bilinear methods [4]. Among these ways, Hirota bilinear method plays an important role in presenting lump solutions owing to its simplicity and directness. Hirota bilinear method plays an important role in presenting lump solutions owing to its simplicity and directness In these solutions, lump solutions are a kind of regular and rationally function solutions, localized in all directions in the space [5].
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