This paper studies the(2+1)-dimensional Hirota-Satsuma-Ito equation.Based on an associated Hirota bilinear form,lump-type solution,two types of interaction solutions,and breather wave solution of the(2+1)-dimensional ...This paper studies the(2+1)-dimensional Hirota-Satsuma-Ito equation.Based on an associated Hirota bilinear form,lump-type solution,two types of interaction solutions,and breather wave solution of the(2+1)-dimensional Hirota-Satsuma-Ito equation are obtained,which are all related to the seed solution of the equation.It is interesting that the rogue wave is aroused by the interaction between one-lump soliton and a pair of resonance stripe solitons,and the fusion and fission phenomena are also found in the interaction between lump solitons and one-stripe soliton.Furthermore,the breather wave solution is also obtained by reducing the two-soliton solutions.The trajectory and period of the one-order breather wave are analyzed.The corresponding dynamical characteristics are demonstrated by the graphs.展开更多
为了促进冰雹灾害等级评估工作的高效进行,提出一种测量冰雹特征参数的方法。该方法统计冰雹图片的HSI颜色范围,用先验的颜色范围来分割出冰雹并通过形态学滤除噪声,针对冰雹颗粒粘连情况运用基于分水岭算法分割边界。分别采用统计像素...为了促进冰雹灾害等级评估工作的高效进行,提出一种测量冰雹特征参数的方法。该方法统计冰雹图片的HSI颜色范围,用先验的颜色范围来分割出冰雹并通过形态学滤除噪声,针对冰雹颗粒粘连情况运用基于分水岭算法分割边界。分别采用统计像素法、Freeman链码和改进的最小外接矩形法来测量冰雹颗粒的面积、周长和直径并与相关算法进行了实验比较。实验结果表明该方法精准度高、相关性较好,冰雹周长、面积和直径的均方根误差(Root Mean Square Error,RMSE)分别为0.2081 cm、0.2124 cm 2和0.9314 cm,决定系数(R 2)分别为0.8814、0.8736和0.9314,测量值平均误差在2%~6%之间。研究结果可为冰雹灾害相关的研究者提供准确的数据参考。展开更多
This article investigates the Hirota-Satsuma-Ito equation with variable coefficient using the Hirota bilinear method and the long wave limit method.The equation is proved to be Painlevé integrable by Painlevé...This article investigates the Hirota-Satsuma-Ito equation with variable coefficient using the Hirota bilinear method and the long wave limit method.The equation is proved to be Painlevé integrable by Painlevé analysis.On the basis of the bilinear form,the forms of two-soliton solutions,three-soliton solutions,and four-soliton solutions are studied specifically.The appropriate parameter values are chosen and the corresponding figures are presented.The breather waves solutions,lump solutions,periodic solutions and the interaction of breather waves solutions and soliton solutions,etc.are given.In addition,we also analyze the different effects of the parameters on the figures.The figures of the same set of parameters in different planes are presented to describe the dynamical behavior of solutions.These are important for describing water waves in nature.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant Nos.12275172 and 11905124)。
文摘This paper studies the(2+1)-dimensional Hirota-Satsuma-Ito equation.Based on an associated Hirota bilinear form,lump-type solution,two types of interaction solutions,and breather wave solution of the(2+1)-dimensional Hirota-Satsuma-Ito equation are obtained,which are all related to the seed solution of the equation.It is interesting that the rogue wave is aroused by the interaction between one-lump soliton and a pair of resonance stripe solitons,and the fusion and fission phenomena are also found in the interaction between lump solitons and one-stripe soliton.Furthermore,the breather wave solution is also obtained by reducing the two-soliton solutions.The trajectory and period of the one-order breather wave are analyzed.The corresponding dynamical characteristics are demonstrated by the graphs.
文摘为了促进冰雹灾害等级评估工作的高效进行,提出一种测量冰雹特征参数的方法。该方法统计冰雹图片的HSI颜色范围,用先验的颜色范围来分割出冰雹并通过形态学滤除噪声,针对冰雹颗粒粘连情况运用基于分水岭算法分割边界。分别采用统计像素法、Freeman链码和改进的最小外接矩形法来测量冰雹颗粒的面积、周长和直径并与相关算法进行了实验比较。实验结果表明该方法精准度高、相关性较好,冰雹周长、面积和直径的均方根误差(Root Mean Square Error,RMSE)分别为0.2081 cm、0.2124 cm 2和0.9314 cm,决定系数(R 2)分别为0.8814、0.8736和0.9314,测量值平均误差在2%~6%之间。研究结果可为冰雹灾害相关的研究者提供准确的数据参考。
基金This work was supported by the National Natural Science Foundation of China(Grant No.11505090)Research Award Foundation for Outstanding Young Scientists of Shandong Province(Grant No.BS2015SF009)+2 种基金the Doctoral Foundation of Liaocheng University(Grant No.318051413)Liaocheng University Level Science and Technology Research Fund(Grant No.318012018)Discipline with Strong Characteristics of Liaocheng University–Intelligent Science and Technology(Grant No.319462208).
文摘This article investigates the Hirota-Satsuma-Ito equation with variable coefficient using the Hirota bilinear method and the long wave limit method.The equation is proved to be Painlevé integrable by Painlevé analysis.On the basis of the bilinear form,the forms of two-soliton solutions,three-soliton solutions,and four-soliton solutions are studied specifically.The appropriate parameter values are chosen and the corresponding figures are presented.The breather waves solutions,lump solutions,periodic solutions and the interaction of breather waves solutions and soliton solutions,etc.are given.In addition,we also analyze the different effects of the parameters on the figures.The figures of the same set of parameters in different planes are presented to describe the dynamical behavior of solutions.These are important for describing water waves in nature.
