Bounded Traveling Wave Solutions of a (2+1)-Dimensional Breaking Soliton Equation

IF 1.2 4区 数学 Q2 MATHEMATICS, APPLIED
Fuli Tian
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引用次数: 0

Abstract

. We qualitatively analyze the bounded traveling wave solutions of a (2 + 1)- dimensional generalized breaking soliton (gBS) equation by using the theory of planar dynamical systems. We present the global phase diagrams of the dynamical system corresponding to the (2 + 1)-dimensional gBS equation under different parameters. The conditions for the existence of bounded traveling wave solutions are successfully derived. We find the relationship between the waveform of bounded traveling wave solutions and the dissipation coefficient β . When the absolute value of the dissipation coefficient β is greater than a critical value, we find that the equation has a kink profile solitary wave solution, while the solution has oscillatory and damped property if | β | is less than the critical value. In addition, we give the exact bell profile solitary wave solution and kink profile solitary wave solution by using undetermined coefficient method. The approximate oscillatory damped solution is given constructively. Through error analysis, we find that the approximate oscillatory damped solution is meaningful. Finally, we present the graphical analysis of the influence of dissipation coefficient β on oscillatory damped solution in order to better understand their dynamical behaviors.
一类(2+1)维破缺孤立子方程的有界行波解
利用平面动力系统理论,定性地分析了(2+1)维广义破断孤子(gBS)方程的有界行波解。我们给出了(2+1)维gBS方程所对应的动力系统在不同参数下的全局相图。成功地导出了有界行波解存在的条件。我们确定了有界行波解的波形与耗散系数β之间的关系。当耗散系数β的绝对值大于临界值时,我们发现方程具有扭结的孤立波解,而如果|β|小于临界值,则解具有振荡和阻尼性质。此外,我们用待定系数法给出了精确的bell pro-File孤立波解和扭结pro-File孤波解。构造性地给出了近似的振荡阻尼解。通过误差分析,我们发现近似振荡阻尼解是有意义的。最后,我们对耗散系数β对振荡阻尼解的影响进行了图解分析,以更好地了解它们的动力学行为。
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来源期刊
CiteScore
2.60
自引率
8.30%
发文量
48
期刊介绍: The East Asian Journal on Applied Mathematics (EAJAM) aims at promoting study and research in Applied Mathematics in East Asia. It is the editorial policy of EAJAM to accept refereed papers in all active areas of Applied Mathematics and related Mathematical Sciences. Novel applications of Mathematics in real situations are especially welcome. Substantial survey papers on topics of exceptional interest will also be published occasionally.
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