| Citation: |
Weihong Mao. BIFURCATIONS AND EXACT TRAVELLING WAVE SOLUTIONS OF M-N-WANG EQUATION[J]. Journal of Applied Analysis & Computation, 2020, 10(1): 210-222. doi: 10.11948/20190113
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BIFURCATIONS AND EXACT TRAVELLING WAVE SOLUTIONS OF M-N-WANG EQUATION
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Abstract
By using the method of dynamical systems to Mikhailov-Novikov-Wang Equation, through qualitative analysis, we obtain bifurcations of phase portraits of the traveling system of the derivative $\phi(\xi)$ of the wave function $\psi(\xi)$. Under different parameter conditions, for $\phi(\xi)$, exact explicit solitary wave solutions, periodic peakon and anti-peakon solutions are obtained. By integrating known $\phi(\xi)$, nine exact explicit traveling wave solutions of $\psi(\xi)$ are given. -
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References
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Weihong Mao. BIFURCATIONS AND EXACT TRAVELLING WAVE SOLUTIONS OF M-N-WANG EQUATION[J]. Journal of Applied Analysis & Computation, 2020, 10(1): 210-222. doi: 10.11948/20190113
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Figure 1. The bifurcations of phase portraits of system (2.1) for
$ c < 0 $ -
Figure 2. The bifurcations of phase portraits of system (2.1) for
$ c > 0 $ -
Figure 3. The changes of level curves defined by
$ H(\phi, y) = h $ in Fig. 1(c) - Figure 4. Solitary wave, compacton and periodic peakon solutions of system (1.6)
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Figure 5. The changes of level curves defined by
$ H(\phi, y)=h $ in Figure 2(d) - Figure 6. Solitary wave and Anti-peakon solutions of system (1.6)