摘要
近年来,尘埃等离子体的研究在太空、工业和实验室等领域中有着重要的作用.该文从双温尘埃等离子体的控制方程组出发,通过运用多尺度分析与约化摄动方法,推导了(2+1)维的Kadomtsev-Petviashvili(KP)方程来描述双温尘埃等离子体声波的传播.接下来,利用半逆方法和分数变分原理,将(2+1)维KP方程推广到时空分数阶KP方程;分数阶KP方程对于描述实际问题中的物理现象具有潜在的应用价值.进一步,基于李对称分析方法,讨论了时间分数阶KP方程的守恒律,得到了双温尘埃等离子体声波的守恒量.最后,基于双线性方法,获得了分数阶KP方程的Lump解.该解的存在说明双温尘埃等离子体中存在怪波,特别地,分析了分数阶阶数对怪波的影响.
In recent years, the dust plasma research plays an important role in the field of space, industry, and laboratory. In this paper, starting from the control equations of the double temperature dust plasma, we derive the(2+1)-dimensional Kadomtsev-Petviashvili(KP) equation to describe the double temperature dust plasma sound waves by using the multi-scale analysis, and reduce it by using the perturbation method. Then by using the semi inverse method and fractional variational principle, the(2+1)-dimensional KP equation is introduced into the time-space fractional KP equation(TFS-KP). The fractional KP equation has potential applications in describing physical phenomena in practical problems. Furthermore, based on the symmetrical analysis method,by which lie discussed the time fractional KP(TF-KP) equation of the conservation law, the dual temperature dust plasma acoustic conserves quantity. Finally, based on the bilinear method, the lump solution of fractional KP equation is obtained. The existence of this solution indicates the rogue waves existing in double temperature dusty plasma. The influence of fractional order on rogue wave is also analyzed.
作者
孙俊超
张宗国
董焕河
杨红卫
Sun Jun-Chao;Zhang Zong-Guo;Dong Huan-He;Yang Hong-Wei(revised manuscript received 17 September 2019;School of Mathematics Statistics,Qilu University of Technology (Shandong Academy of Sciences),Jinan 250353,China)
出处
《物理学报》
SCIE
EI
CAS
CSCD
北大核心
2019年第21期15-25,共11页
Acta Physica Sinica
基金
国家自然科学基金(批准号:11975143)
山东省自然科学基金(批准号:ZR2018MA017)
山东科技大学研究生科技创新项目(批准号:SDKDYC190238)资助的课题~~
