构造维数约化的变系数的B-type KP方程的解（英文）
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摘要
本文研究了流体动力学中一个一般形式的(3+1)维的非线性变系数的B-type KP方程解的问题.利用双线性化及符号计算的方法,获得了维约化后的一般形式的(3+1)维的非线性变系数的B-type KP方程解,并用三维立体图形和等值线图将所求解的性质形象地展示出来.
In this paper, we investigate a generalized(3+1)-dimensional variable-coefficient B-type Kadomtsev-Petviashvili equation in fluid dynamics. Based on bilinear forms, the solutions to dimensionally reduced generalized variable coefficient B-type Kadomtsev-Petviashvili equation in(3+1)-dimensions are computed through symbolic computation. The property of solutions is investigated and exhibited vividly by three dimensional plots and contour plots.
In this paper, we investigate a generalized(3+1)-dimensional variable-coefficient B-type Kadomtsev-Petviashvili equation in fluid dynamics. Based on bilinear forms, the solutions to dimensionally reduced generalized variable coefficient B-type Kadomtsev-Petviashvili equation in(3+1)-dimensions are computed through symbolic computation. The property of solutions is investigated and exhibited vividly by three dimensional plots and contour plots.
引文
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[2] Ablowitz M J, Clarkson P A. Solitions, nonlinear evolution equations and inverse scattering[M].Cambridge:Cambridge Univ. Press, 1991.
[3] Bekir A. Painlev′e test for some(2+1)-dimensional nonlinear equations[J]. Chaos Soli. Frac., 2007,32(2):449–455.
[4] Matveeev V B, Salle M A. Darboux transformations and solitions[M]. Berlin:Springers, 1991.
[5] Hirota R. The direct method in solition theory[M]. Cambridge:Cambridge Univ. Press, 2004.
[6] Xing L, Ma W X, Khalique C M. A direct bilinear B¨acklund transformation of a(2+1)-dimensional Korteweg-de vries-like model[J]. Appl. Math. Lett., 2015, 50:37–42.
[7] Ma W X. Trilinear equations, Bell polynomials, and resonant solutions[J]. Front. Math. China, 2013,8(5):1139–1156.
[8] Zhang H. A note on exact complex travelling wave solutions for(2+1)-dimensional B-type Kadomtsev-Petviashvili equation[J]. Appl. Math. Comput., 2010, 216(9):2771–2777.
[9] Ma W X. Lump solutions to the Kadomtsev-Petviashvili equation[J]. Phys. Lett. A, 2015, 379(36):1975–1978.
[10] Matveev V B. Generalized Wronskian formula for solutions of the KdV equations:first applications[J]. Phys. Lett. A, 1992, 166(3-4):205–208.
[11] Gao X Y. B¨acklund transformation and shock-wave-type solutions for a generalized(3+1)-dimensional variable-coefficient B-type Kadomtsev-Petviashvili equation in fluid mechanics[J].Ocean Engin., 2015, 96:245–247.
[12] Bell E T. Exponential polynomials[J]. Ann. Math., 1934, 35(2):258–277.
[2] Ablowitz M J, Clarkson P A. Solitions, nonlinear evolution equations and inverse scattering[M].Cambridge:Cambridge Univ. Press, 1991.
[3] Bekir A. Painlev′e test for some(2+1)-dimensional nonlinear equations[J]. Chaos Soli. Frac., 2007,32(2):449–455.
[4] Matveeev V B, Salle M A. Darboux transformations and solitions[M]. Berlin:Springers, 1991.
[5] Hirota R. The direct method in solition theory[M]. Cambridge:Cambridge Univ. Press, 2004.
[6] Xing L, Ma W X, Khalique C M. A direct bilinear B¨acklund transformation of a(2+1)-dimensional Korteweg-de vries-like model[J]. Appl. Math. Lett., 2015, 50:37–42.
[7] Ma W X. Trilinear equations, Bell polynomials, and resonant solutions[J]. Front. Math. China, 2013,8(5):1139–1156.
[8] Zhang H. A note on exact complex travelling wave solutions for(2+1)-dimensional B-type Kadomtsev-Petviashvili equation[J]. Appl. Math. Comput., 2010, 216(9):2771–2777.
[9] Ma W X. Lump solutions to the Kadomtsev-Petviashvili equation[J]. Phys. Lett. A, 2015, 379(36):1975–1978.
[10] Matveev V B. Generalized Wronskian formula for solutions of the KdV equations:first applications[J]. Phys. Lett. A, 1992, 166(3-4):205–208.
[11] Gao X Y. B¨acklund transformation and shock-wave-type solutions for a generalized(3+1)-dimensional variable-coefficient B-type Kadomtsev-Petviashvili equation in fluid mechanics[J].Ocean Engin., 2015, 96:245–247.
[12] Bell E T. Exponential polynomials[J]. Ann. Math., 1934, 35(2):258–277.