| Citation: |
Yanzhi Ma, Zenggui Wang. TRAVELING WAVE SOLUTIONS, POWER SERIES SOLUTIONS AND CONSERVATION LAWS OF THE NONLINEAR DISPERSION EQUATION[J]. Journal of Applied Analysis & Computation, 2023, 13(4): 2267-2282. doi: 10.11948/20220470
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TRAVELING WAVE SOLUTIONS, POWER SERIES SOLUTIONS AND CONSERVATION LAWS OF THE NONLINEAR DISPERSION EQUATION
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Abstract
In this paper, the nonlinear dispersive equation is investigated by Lie symmetry analysis theory and bifurcation theory. The infinitesimal generators of the equation are obtained by Lie symmetry analysis. Periodic peakon solutions, single period solutions and power series solutions of the equation are acquired. And the conservation laws are obtained by the Ibragimov's method.
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References
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Yanzhi Ma, Zenggui Wang. TRAVELING WAVE SOLUTIONS, POWER SERIES SOLUTIONS AND CONSERVATION LAWS OF THE NONLINEAR DISPERSION EQUATION[J]. Journal of Applied Analysis & Computation, 2023, 13(4): 2267-2282. doi: 10.11948/20220470
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Figure 1.
phase portraits of (3.5) for
$ {k = 0} $ $ {c>0} $ $ {\beta>0} $ $ {c<0} $ $ {\beta>0} $ $ {c>0} $ $ {\beta<0} $ $ {c<0} $ $ {\beta<0} $ -
Figure 2.
phase portraits of (3.5) for
$ k\neq0 $ $ c>0 $ $ \beta>0 $ $ -\dfrac{4c^2}{9\beta}<k<0 $ $ \beta<0 $ $ c>0 $ $ k = -\dfrac{4c^2}{9\beta} $ $ \beta>0 $ $ c>0 $ $ k>-\dfrac{4c^2}{9\beta} $ -
Figure 3.
(a) The 3D plot of
$ \psi $ $ \beta>0, $ $ c>0 $ -
Figure 4.
(a) The 3D plot of
$ \psi $ $ \beta>0, $ $ c>0 $ -
Figure 5.
(a) The 3D plot of
$ \psi $ $ \psi $ $ t = 1 $ $ t = 5 $ $ t = 10 $ $ \psi $ $ x = 1 $ $ x = 5 $ $ x = 10 $ -
Figure 6.
(a) The 3D plot of
$ \psi $