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Bifurcation of Traveling Wave Solutions and Dynamical Behaviors of a Class of K (m, n) Equations with Generalized Evolution Terms

Author: YinLan
Tutor: ZhangWeiPeng
School: Northeast Normal University
Course: Applied Mathematics
Keywords: Bifurcation curve Singular traveling wave equation Solitary wave Smooth periodicwave Periodic cusp wave
CLC: O175.29
Type: Master's thesis
Year: 2011
Downloads: 18
Quote: 0
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Abstract


In this paper, by using bifurcation theory and methods of plane dynamic system, we investigate thebifurcation and dynamical behavior of some special cases of a class of K(m, n) equations, i.e. (ul)t +aumux +(?), n = 2, l≥2. We obtain some exact explicit parametric representations oftraveling wave solutions by using time scaling transformation. We convert K(m, n) equation into a regularsystem, then the bifurcation and dynamical behaviors of regular system is discussed using bifurcation theoryof dynamic system. By discussing regular system, we find the existence of traveling wave solution anddynamical behavior of the singular traveling wave system. Meanwhile we get some exact traveling waveand the existence of periodic solution.

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CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Differential equations, integral equations > Partial Differential Equations > Nonlinear partial differential equations
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