Yan Zhenya, Zhang Hongqing. Similarity Reductions for 2+1-Dimensional Variable Coefficient Generalized Kadomtsev-Petviashvili Equation[J]. Applied Mathematics and Mechanics, 2000, 21(6): 585-589.
Citation:
Yan Zhenya, Zhang Hongqing. Similarity Reductions for 2+1-Dimensional Variable Coefficient Generalized Kadomtsev-Petviashvili Equation[J]. Applied Mathematics and Mechanics, 2000, 21(6): 585-589.
Yan Zhenya, Zhang Hongqing. Similarity Reductions for 2+1-Dimensional Variable Coefficient Generalized Kadomtsev-Petviashvili Equation[J]. Applied Mathematics and Mechanics, 2000, 21(6): 585-589.
Citation:
Yan Zhenya, Zhang Hongqing. Similarity Reductions for 2+1-Dimensional Variable Coefficient Generalized Kadomtsev-Petviashvili Equation[J]. Applied Mathematics and Mechanics, 2000, 21(6): 585-589.
Similarity Reductions for 2+1-Dimensional Variable Coefficient Generalized Kadomtsev-Petviashvili Equation
Received Date: 1999-03-02
Rev Recd Date:
1999-12-13
Publish Date:
2000-06-15
Abstract
With the aid of MATHEMATICA,the direct reduction method was extended and applied in 2+1-dimensional variable coefficient generalized Kadomtsev-Petviashvili equation(VCGKPE).As a result,several kinds of similarity reductions for VCGKPE are obtained which contain PainleveⅠ,Painleve Ⅱ and PainleveⅣ reductions.
References
[1]
Clarkson P A,Kruskal M D.New similarity reductions of the Boussinesq equation[J].J Math Phys,1989,30(10):2201~2212.
[2]
Zhang J F,Zhu Y J,Lin J.Similarity reductions for the Khokhlov-Zabolotskaya equation[J].Commun Theor Phys,1995,22(1):69~74.
[3]
Ruan H Y,Lou S Y.Similarity reductions and Painleve properties for the Kupershmidt equation[J].Commun Theor Phys,1993,20(1):73~80.
[4]
阮航宇,楼森岳.Whitham-Broer-Kaup 浅水波方程的对称性约化[J].物理学报,1992,41(8):1213~1219.
[5]
谷超豪,李翊神,田畴,等.孤立子理论与应用[M].杭州:浙江科学技术出版社,1990.
[6]
Ablowitz M J,Clarkson P A.Solitons,Nonlinear Evolution Equations and Inverse Scattering[M].New York:Cambridge University Press,1991.
[7]
Wang M L,Zhou Y B,Li Z B.Application of a homogeneous blance method to exact solutions of nonlinear equations in mathematical physics[J].Phys Lett A,1996,216(1):67~73.
[8]
Lou S Y.Painlev test for the integrable dispersive long wave equations in two space dimensions[J].Phys Lett A,1993,176(1):96~102.
Relative Articles
[1] LIU Mian, CHENG Hao, SHI Chengxin. Variational Regularization of the Inverse Problem of a Class of Nonlinear Time-Fractional Diffusion Equations [J]. Applied Mathematics and Mechanics, 2022, 43(3): 341-352. doi: 10.21656/1000-0887.420168
[2] LEI Yang, FENG Jianhu. Topology Optimization of Nonlinear Material Structures Based on Parameterized Level Set and Substructure Methods [J]. Applied Mathematics and Mechanics, 2021, 42(11): 1150-1160. doi: 10.21656/1000-0887.420090
[3] WANG Zhao-ling>, XIAO Heng. A New Development of Reduced Hamiltonian Equations for Ocean Surface Waves: an Extension From Small to Finite Amplitude [J]. Applied Mathematics and Mechanics, 2015, 36(11): 1135-1144. doi: 10.3879/j.issn.1000-0887.2015.11.002
[4] ZHANG Qiao-fu, CUI Jun-zhi. Existence Theory for Rosseland Equation and Its Homogenized Equation [J]. Applied Mathematics and Mechanics, 2012, 33(12): 1487-1502. doi: 10.3879/j.issn.1000-0887.2012.12.010
[5] GONG Zhao-xin, LU Chuan-jing, HUANG Hua-xiong. Effect of the Regularized Delta Function on the Accuracy of the Immersed Boundary Method [J]. Applied Mathematics and Mechanics, 2012, 33(11): 1352-1365. doi: 10.3879/j.issn.1000-0887.2012.11.010
[6] Abdul-Majid Wazwaz. Multiple-Front Waves for Extended Form of Modified Kadomtsev-Petviashvili Equation [J]. Applied Mathematics and Mechanics, 2011, 32(7): 821-825. doi: 10.3879/j.issn.1000-0887.2011.07.006
[7] QIN Yan-mei, FENG Min-fu, LUO Kun, WU Kai-teng. Local Projection Stabilized Finite Element Method for the Navier-Stokes Equations [J]. Applied Mathematics and Mechanics, 2010, 31(5): 618-630. doi: 10.3879/j.issn.1000-0887.2010.05.013
[8] CHEN Yu-mei, XIE Xiao-ping. Streamline Diffusion Nonconforming Finite Element Method for the Time-Dependent Linearized Navier-Stokes Equations [J]. Applied Mathematics and Mechanics, 2010, 31(7): 822-834. doi: 10.3879/j.issn.1000-0887.2010.07.007
[9] FENG Min-fu, YANG Yan, ZHOU Tian-xiao. Nonconforming Stabilized Combined Finite Element Method for the Reissner-Mindlin Plate [J]. Applied Mathematics and Mechanics, 2009, 30(2): 192-202.
[10] ZHOU Huan-lin, NIU Zhong-rong, WANG Xiu-xi. Regularization of Nearly Singular Integrals in the Boundary Element Method of Potential Problems [J]. Applied Mathematics and Mechanics, 2003, 24(10): 1069-1074.
[11] XIE Fu-ding, YAN Zhen-ya, ZHANG Hong-qing. Similarity Reductions for the Nonlinear Evolution Equation Arising in the Fermi-Pasta-Ulam Problem [J]. Applied Mathematics and Mechanics, 2002, 23(4): 347-352.
[12] ZHENG Quan-shui, ZOU Wen-nan. Orientation Distribution Functions for Microstructures of Heterogeneous Materials(Ⅰ)-Directional Distribution Functions and Irreducible Tensors [J]. Applied Mathematics and Mechanics, 2001, 22(8): 773-789.
[13] TIAN Li-xin, CHU Zhi-jun, LIU Zeng-rong, JIANG Yong. Numerical Analysis of Longtime Dynamic Behavior in Weakly Damped Forced KdV Equation [J]. Applied Mathematics and Mechanics, 2000, 21(10): 1013-1020.
[14] Huang Debin, Zhao Xiaohua. The Vector Fields Admitting One-Parameter Spatial Symmetry Group and Their Reduction [J]. Applied Mathematics and Mechanics, 2000, 21(2): 154-160.
[15] Lin Yurui, Tian Lixin, Liu Zengrong. The Wild Solutions of the Induced Form under the Spline Wavelet Basis in Weakly Damped Forced KdV Equation [J]. Applied Mathematics and Mechanics, 1998, 19(12): 1071-1076.
[16] Wei Zhiyong, Zhu Yongtai. The Extended Jordan’s Lemma and the Relation between Laplace Transform and Fourier Transform [J]. Applied Mathematics and Mechanics, 1997, 18(6): 531-534.
[17] Ji Zhen-yi, Ye Kai-yuan. A High Convergent Precision Exact Analytic Method for Differential Equation with Variable Coefficients [J]. Applied Mathematics and Mechanics, 1993, 14(3): 189-194.
[18] Wang You-cheng, Wang Zuo-hui. Isotropicalized Spline Integral Equation Method for the Analysis of Anisotropic Plates [J]. Applied Mathematics and Mechanics, 1990, 11(9): 779-784.
[19] Ji Zhen-yi, Ye Kai-yuan. Exact Analytic Method for Solving Variable Coefficient Differential Equation [J]. Applied Mathematics and Mechanics, 1989, 10(10): 841-852.
[20] Tsai Shu-tang, Liu Yi-xin. Similarity Problem of Inceptive Cavitation [J]. Applied Mathematics and Mechanics, 1985, 6(11): 963-968.
Proportional views
Created with Highcharts 5.0.7 Chart context menu Access Class Distribution FULLTEXT : 20.8 % FULLTEXT : 20.8 % META : 77.6 % META : 77.6 % PDF : 1.6 % PDF : 1.6 % FULLTEXT META PDF
Created with Highcharts 5.0.7 Chart context menu Access Area Distribution 其他 : 6.5 % 其他 : 6.5 % China : 0.8 % China : 0.8 % Singapore : 0.1 % Singapore : 0.1 % 上海 : 0.7 % 上海 : 0.7 % 北京 : 2.2 % 北京 : 2.2 % 南宁 : 0.1 % 南宁 : 0.1 % 哥伦布 : 0.3 % 哥伦布 : 0.3 % 宣城 : 0.3 % 宣城 : 0.3 % 张家口 : 1.0 % 张家口 : 1.0 % 昆明 : 0.6 % 昆明 : 0.6 % 昭通 : 0.2 % 昭通 : 0.2 % 武汉 : 0.1 % 武汉 : 0.1 % 洛杉矶 : 0.4 % 洛杉矶 : 0.4 % 深圳 : 0.2 % 深圳 : 0.2 % 漯河 : 0.2 % 漯河 : 0.2 % 石家庄 : 0.7 % 石家庄 : 0.7 % 芒廷维尤 : 4.5 % 芒廷维尤 : 4.5 % 苏州 : 0.1 % 苏州 : 0.1 % 西宁 : 80.1 % 西宁 : 80.1 % 西安 : 0.1 % 西安 : 0.1 % 郑州 : 0.5 % 郑州 : 0.5 % 阳泉 : 0.1 % 阳泉 : 0.1 % 其他 China Singapore 上海 北京 南宁 哥伦布 宣城 张家口 昆明 昭通 武汉 洛杉矶 深圳 漯河 石家庄 芒廷维尤 苏州 西宁 西安 郑州 阳泉