| Citation: |
Yuanqing Xu, Xiaoxiao Zheng, Jie Xin. ABUNDANT NEW NON-TRAVELING WAVE SOLUTIONS FOR THE (3+1)-DIMENSIONAL BOITI-LEON-MANNA-PEMPINELLI EQUATION[J]. Journal of Applied Analysis & Computation, 2021, 11(4): 2052-2069. doi: 10.11948/20200314
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ABUNDANT NEW NON-TRAVELING WAVE SOLUTIONS FOR THE (3+1)-DIMENSIONAL BOITI-LEON-MANNA-PEMPINELLI EQUATION
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Abstract
Seeking exact solutions of higher-dimensional nonlinear partial differential equations has recently received tremendous attention in mathematics and physics. In this paper, we investigate exact solutions of (3+1)-dimensional Boiti-Leon-Manna-Pempinelli equation which describes nonlinear wave propagation in incompressible fluid. Firstly, by means of extended homoclinic test approach, we get eight kinds of non-traveling wave solutions of (3+1)-dimensional Boiti-Leon-Manna-Pempinelli equation. Then, combining the improved tanh function method and new ansatz solutions, we obtain abundant new exact non-traveling wave solutions of (3+1)-dimensional Boiti-Leon-Manna-Pempinelli equation. These results include not only many results obtained in other literatures, but also some new exact non-traveling wave solutions. Moreover, the exact kink wave solutions, periodic solitary wave solutions and singular solitary wave solutions are given when arbitrary functions contained in these solutions are taken as some special functions.
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References
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Yuanqing Xu, Xiaoxiao Zheng, Jie Xin. ABUNDANT NEW NON-TRAVELING WAVE SOLUTIONS FOR THE (3+1)-DIMENSIONAL BOITI-LEON-MANNA-PEMPINELLI EQUATION[J]. Journal of Applied Analysis & Computation, 2021, 11(4): 2052-2069. doi: 10.11948/20200314
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Figure 1. Exact kink type solitary solution for
$ u_{1} $ as$ a_{2} = -1, k_{2} = 1, n = 3, m = c = 0, \theta (z) = z, x = y = 0. $ -
Figure 2. Kink-like solution with a parabolic tail for
$ u_{1} $ as$ a_{2} = -1, k_{2} = m = 1, n = 3, c = 0, \theta (z) = z^{2}, x = y = 0. $ -
Figure 3. Exact singular solitary wave solution for
$ u_{2} $ as$ a_{2} = k_{2} = -1, n = 3, m = c = 0, \theta (z) = z, x = y = 0. $ -
Figure 4. Singular solitary wave-like solution with a parabolic tail for
$ u_{2} $ as$ a_{2} = k_{2} = -1, m = 1, n = 3, c = 0, \theta (z) = z^{2}, x = y = 0. $ -
Figure 5. Periodic solitary wave-like solution for
$ u_{3} $ with a parabolic tail as$ a_{1} = k_{1} = m = 1, k_{2} = 2, n = 3, c = 0, \theta (z) = z^{2}, x = y = 0. $ -
Figure 6. Singular solitary wave-like solution with a parabolic tail for
$ u_{7} $ as$ a_{1} = i, a_{2} = ia_{1} = -1, k_{1} = -0.5, k_{3} = m = 1, n = 3, c = 0, \theta (z) = z^{2}, x = y = 0. $