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Lump wave and hybrid solutions of a generalized(3+1)-dimensional nonlinear wave equation in liquid with gas bubbles |
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| Authors: | Hui WANG Shoufu TIAN Tiantian ZHANG Yi CHEN |
| Affiliation: | School of Mathematics and Institute of Mathematical Physics, China University of Mining and Technology, Xuzhou 221116, China |
| Abstract: | We investigate a generalized (3+ 1)-dimensional nonlinear wave equation, which can be used to depict many nonlinear phenomena in liquid containing gas bubbles. By employing the Hirota bilinear method, we derive its bilinear formalism and soliton solutions succinctly. Meanwhile, the first-order lump wave solution and second-order lump wave solution are well presented based on the corresponding two-soliton solution and four-soliton solution. Furthermore, two types of hybrid solutions are systematically established by using the long wave limit method. Finally, the graphical analyses of the obtained solutions are represented in order to better understand their dynamical behaviors. |
| Keywords: | Generalized (3+ 1)-dimensional nonlinear wave equation bilinear formalism soliton solutions lump solutions hybrid solutions |
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