| Citation: |
Huizhang Yang, Wei Liu, Bin He. EVOLUTIONARY BEHAVIOR OF THE INTERACTION SOLUTIONS FOR A (3+1)-DIMENSIONAL GENERALIZED BREAKING SOLITON EQUATION[J]. Journal of Applied Analysis & Computation, 2023, 13(3): 1429-1448. doi: 10.11948/20220212
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EVOLUTIONARY BEHAVIOR OF THE INTERACTION SOLUTIONS FOR A (3+1)-DIMENSIONAL GENERALIZED BREAKING SOLITON EQUATION
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Abstract
The interaction solutions have attracted the attention of many scholars because of they are valuable in analyzing the nonlinear dynamics of waves in shallow water and can be used for forecasting the appearance of rogue waves. In this paper, we investigate the interaction and rational solutions of a (3+1)-dimensional generalized breaking soliton equation by employing the Hirota bilinear and parameter limit methods along with symbolic computations. By studying the Hirota bilinear form of the equation, abundant interaction and rational solutions are derived by choosing appropriate parameters of the test function. The evolutionary behavior of the interaction solutions is also analyzed theoretically and graphically. Compare with the published literatures, we get some completely new results of the equation in this paper.
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References
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Huizhang Yang, Wei Liu, Bin He. EVOLUTIONARY BEHAVIOR OF THE INTERACTION SOLUTIONS FOR A (3+1)-DIMENSIONAL GENERALIZED BREAKING SOLITON EQUATION[J]. Journal of Applied Analysis & Computation, 2023, 13(3): 1429-1448. doi: 10.11948/20220212
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Figure 1.
Three-dimensional and contour plots of (3.8).
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Figure 2.
The limiting precess of (3.7) tends to (3.8) when
$ p_1\rightarrow0. $ $ p_1=1, p_2=1, a_2=\cos(1) $ $ p_1=0.6, p_2=0.6, a_2=\cos(0.6) $ $ p_1=0.3, p_2=0.3, a_2=\cos(0.3) $ $ p_1=0.01, p_2=0.01, a_2=\cos(0.01) $ -
Figure 3.
The limiting precess of (3.9) tends to (3.8) when
$ p_1\rightarrow0. $ $ p_1=0.6, \bar{p}_2=0.6, a_2=\cosh(0.6) $ $ p_1=0.2, \bar{p}_2=0.2, a_2=\cosh(0.2) $ $ p_1=0.07, \bar{p}_2=0.07, a_2=\cosh(0.07) $ $ p_1=0.001, \bar{p}_2=0.001, a_2=\cosh(0.001) $ -
Figure 4.
Three-dimensional and contour plots of (3.11).
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Figure 5.
The limiting precess of (3.10) tends to (3.11) when
$ p_1\rightarrow0. $ $ p_1=1, p_2=1, a_2=\cos(1) $ $ p_1=0.7, p_2=0.7, a_2=\cos(0.7) $ $ p_1=0.5, p_2=0.5, a_2=\cos(0.5) $ $ p_1=0.05, p_2=0.05, a_2=\cos(0.05) $ -
Figure 6.
Three-dimensional and contour plots of (3.13).
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Figure 7.
The limiting precess of (3.12) tends to (3.13) when
$ p_2\rightarrow0. $ $ p_2=0.35, p_3=0.35, a_2=\cos(0.35), a_3=\cosh(0.35) $ $ p_2=0.22, p_3=0.22, a_2=\cos(0.22), a_3=\cosh(0.22) $ $ p_2=0.12, p_3=0.12, a_2=\cos(0.12), a_3=\cosh(0.12) $ $ p_2=0.01, p_3=0.01, a_2=\cos(0.01), a_3=\cosh(0.01) $ -
Figure 8.
Three-dimensional and contour plots of (3.15).
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Figure 9.
The limiting precess of (3.14) tends to (3.15) when
$ \bar{p}_2\rightarrow0. $ $ \bar{p}_2=0.77, p_3=0.77, a_2=\cosh(0.77), a_3=\cosh(0.77) $ $ \bar{p}_2=0.6, p_3=0.6, a_2=\cosh(0.6), a_3=\cosh(0.6) $ $ \bar{p}_2=0.4, p_3=0.4, a_2=\cosh(0.4), a_3=\cosh(0.4) $ $ \bar{p}_2=0.02, p_3=0.02, a_2=\cosh(0.02), a_3=\cosh(0.02) $ -
Figure 10.
The limiting precess of (3.16) tends to (3.15) when
$ p_2\rightarrow0. $ $ p_2=0.7, \bar{p}_3=0.7, a_2=\cos(0.7), a_3=\cos(0.7) $ $ p_2=0.4, \bar{p}_3=0.4, a_2=\cos(0.4), a_3=\cos(0.4) $ $ p_2=0.12, \bar{p}_3=0.12, a_2=\cos(0.12), a_3=\cos(0.12) $ $ p_2=0.02, \bar{p}_3=0.02, a_2=\cos(0.02), a_3=\cos(0.02) $ -
Figure 11.
Three-dimensional and contour plots of (3.18).
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Figure 12.
The limiting precess of (3.17) tends to (3.18) when
$ p_2\rightarrow0. $ $ p_2=1, p_3=1, a_2=\cos(1), a_3=\cosh(1) $ $ p_2=0.6, p_3=0.6, a_2=\cos(0.6), a_3=\cosh(0.6) $ $ p_2=0.4, p_3=0.4, a_2=\cos(0.4), a_3=\cosh(0.4) $ $ p_2=0.04, p_3=0.04, a_2=\cos(0.04), a_3=\cosh(0.04) $ -
Figure 13.
Three-dimensional and contour plots of (3.20).
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Figure 14.
The limiting precess of (3.19) tends to (3.20) when
$ \bar{p}_2\rightarrow0. $ $ \bar{p}_2=1, p_3=1, a_2=\cosh(1), a_3=\cosh(1) $ $ \bar{p}_2=0.6, p_3=0.6, a_2=\cosh(0.6), a_3=\cosh(0.6) $ $ \bar{p}_2=0.45, p_3=0.45, a_2=\cosh(0.45), a_3=\cosh(0.45) $ $ \bar{p}_2=0.05, p_3=0.05, a_2=\cosh(0.05), a_3=\cosh(0.05) $ -
Figure 15.
The limiting precess of (3.21) tends to (3.20) when
$ p_2\rightarrow0. $ $ p_2=1, \bar{p}_3=1, a_2=\cos(1), a_3=\cos(1) $ $ p_2=0.6, \bar{p}_3=0.6, a_2=\cos(0.6), a_3=\cos(0.6) $ $ p_2=0.3, \bar{p}_3=0.3, a_2=\cos(0.3), a_3=\cos(0.3) $ $ p_2=0.05, \bar{p}_3=0.05, a_2=\cos(0.05), a_3=\cos(0.05) $ -
Figure 16.
Three-dimensional and contour plots of (3.23).
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Figure 17.
The limiting precess of (3.22) tends to (3.23) when
$ p_1\rightarrow0. $ $ p_1=0.15, p_2=0.15, p_3=0.15, a_2=\cos(0.15), a_3=\cosh(0.15) $ $ p_1=0.1, p_2=0.1, p_3=0.1, a_2=\cos(0.1), a_3=\cosh(0.1) $ $ p_1=0.05, p_2=0.05, p_3=0.05, a_2=\cos(0.05), a_3=\cosh(0.05) $ $ p_1=0.001, p_2=0.001, p_3=0.001, a_2=\cos(0.001), a_3=\cosh(0.001) $ -
Figure 18.
The limiting precess of (3.24) tends to (3.23) when
$ p_1\rightarrow0. $ $ p_1=0.7, \bar{p}_2=0.7, p_3=0.7, a_2=\cosh(0.7), a_3=\cosh(0.7) $ $ p_1=0.2, \bar{p}_2=0.2, p_3=0.2, a_2=\cosh(0.2), a_3=\cosh(0.2) $ $ p_1=0.02, \bar{p}_2=0.02, p_3=0.02, a_2=\cosh(0.02), a_3=\cosh(0.02) $ $ p_1=0.001, \bar{p}_2=0.001, p_3=0.001, a_2=\cosh(0.001), a_3=\cosh(0.001) $ -
Figure 19.
The limiting precess of (3.25) tends to (3.23) when
$ p_1\rightarrow0. $ $ p_1=0.3, p_2=0.3, \bar{p}_3=0.3, a_2=\cos(0.3), a_3=\cos(0.3) $ $ p_1=0.1, p_2=0.1, \bar{p}_3=0.1, a_2=\cos(0.1), a_3=\cos(0.1) $ $ p_1=0.02, p_2=0.02, \bar{p}_3=0.02, a_2=\cos(0.02), a_3=\cos(0.02) $ $ p_1=0.001, p_2=0.001, \bar{p}_3=0.001, a_2=\cos(0.001), a_3=\cos(0.001) $