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

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-06-01 DOI:10.4208/eajam.2022-135.041222

Fuli Tian

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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.

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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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.