期刊文献+

(3+1)-维广义随机KP方程的精确解 被引量:1

Exact Solutions to(3+1)-Dimensional Stochastic Generalized KP Equation
原文传递
导出
摘要 利用统一方式构造非线性偏微分方程行波解的广义Jacobi椭圆函数展开法和Hermite变换来研究(3+1)-维广义随机KP方程,给出了它的随机对偶周期和多孤子解. In the paper, by using the generalized Jacobi elliptic function method, which is used to construct the exact travelling wave solutions of nonlinear partial differential equations in a unified way, and Hermite transformation, some stochastic doubly periodic and multiple soliton solutions to (3+1)-dimensional stochastic generalized KP equation are obtained.
作者 高娃
出处 《数学的实践与认识》 CSCD 北大核心 2010年第8期209-216,共8页 Mathematics in Practice and Theory
基金 内蒙古自然科学基金(200711020118) 国家自然科学基金(10702023)
关键词 广义随机KP方程 HERMITE变换 广义Jacobi椭圆函数展开法 随机对偶 周期解 随机多孤子解 generalized stochastic KP equation hermite transformation generalized jacobi elliptic function stochastic doubly periodic solution stochastic soliton solution
  • 相关文献

参考文献11

  • 1Wadati M. Stochastic Korteweg-de Vries equation[J]. J Phys Soc Jpn, 1983, 52: 2642-2648.
  • 2De Bouard A, Debussche A. On the stochastic Korteweg-de Vries equation[J]. J Funct Anal, 1998, 154: 215-251.
  • 3Printems J. The stochastic Korteweg-de Vries equation in L^2(R)[J]. Journal of Differential Equations, 1999, 153: 338-373.
  • 4Xie Y C. Exact solutions for stochastic KdV equations[J]. Physics Letters A, 2003, 310: 161-167.
  • 5Xie Y C. Exact solutions of the Wick-type stochastic Kadomtsev-Petviashvili equations[J]. Chaos, Solitons and Fractals, 2004, 21: 473-480.
  • 6Wei C M, Xia Z Q and Tian N S. Exact solutions to generalized Wick-type stochastic Kadomtsev- Petviashvili equation[J]. Chaos, Solitons and fractals, 2006, 29(5): 1178-1187.
  • 7Wei C M, Xia Z Q. Exact solutions for (3+1)-dimensional wick-type stochastic KP equation[J]. Journal of Applied Mathematics and Computing, 2006, 21(1-2): 369-377.
  • 8Holden H, Φsendal B, Ubce J, Zhang T. Stochastic partial differential equations[J]. Birhkauser, 1996.
  • 9Benth F E, Gjerde J. A remark on the equivalence between poisson and gaussian stochastic partial differential equations[J]. Potential Analysis, 1998, 8: 179-193.
  • 10Liu S K, Liu S D. Nonlinear Equations in Physics[M]. Peking: Peking University Press, 2000.

二级参考文献25

  • 1Duffy B R and Parkes E J 1996 Phys. Lett. A 214 271.
  • 2Parkes E J and Duffy B R 1997 Phys. Lett. A 229 217.
  • 3Li Z B 2000 Exact solitary wave solutions of nonlinear evolution equations, Mathematics Mechanization and Application ed Gao X S, Wang D M (New York: Academic).
  • 4Li Z B and Wang M L 1993 J. Phys. A: Math. Gen. 26 6027.
  • 5Parkes E J 1994 J. Phys. A: Math. Gen. 27 L497.
  • 6Gardner C S, Greene J M, Kruskal M D and Miura R M 1967 Phys. Rev. Lett. 19 1095.
  • 7Hu X B and Ma W X 2002 Phys. Lett. A 293 161.
  • 8Weis J, Tabor M and Garnevale G 1983 J. Math, Phys.24 522.
  • 9Fan E G and Zhang H Q 1998 Phys. Lett. A 246 403.
  • 10Yang L, Zhu Z and Wang Y 1999 Phys. Lett. A 260 55.

共引文献1

同被引文献21

  • 1Miura M R. Baicklund transformation[M]. Berlin: Springer-Verlag, 1978.
  • 2Gu C H, Hu H S, Zhou Z X. Daxboux transformation in solitons theory and geometry applications[M]. Shanghai: Shanghai Science Technology Press, 1999.
  • 3Hirota R. Exact solution of the Korteweg-de Vries for multiple collisions of solutions[J]. Physical Review Letters, 1971, 27: 1192-1194.
  • 4Wang M L. Solitary wave solutions for variant Boussinesq equations[J]. Physics Letter A, 1996, 199: 169-172.
  • 5Wang M L, Zhou Y B, Li Z B. Application of a homogeneous balance method to exact solutions of nonlinear equations in mathematical physics[J]. Physics letter A, 1996, 216: 67-75.
  • 6Weiss J, Tabor M, Carnevale G. The Painleve Property for Partial Differential Equations[J]. Journal of Mathematical Physics, 1983, 24: 552-564.
  • 7Nayfeh A H. Perturbation Methods[M]. New York: John Wiley and Sons Inc, 1973.
  • 8Liu S K, Fu Z T, Liu S D, et al. Jacobi elliptic function expansion method and periodic wave solutions of nonlinear wave equations [J]. Physics Letter A, 2001, 289: 69-74.
  • 9Fu Z T, Liu S K, Liu S D, et al. The JEFE method and periodic solutions of two kinds of nonlinear wave equations[J]. Communications in Nonlinear Science & Numerical Simulation, 2003, 8: 67-75.
  • 10Yan Z Y. The extended Jacobian elliptic functions expansion method and its application in the generalized Hirota-Satsuma coupled KdV systems[J]. Chaos, Solitons and Fractals, 2003, 15(3): 575-583.

引证文献1

相关作者

内容加载中请稍等...

相关机构

内容加载中请稍等...

相关主题

内容加载中请稍等...

浏览历史

内容加载中请稍等...
;
使用帮助 返回顶部