Abundant similarity reductions and dromion-like solutions to the generalized Kroteweg-de Vries equation in the (2+1)-dimensional space

作者：Yan ZY^*

来源：Communications in Theoretical Physics, 2001, 36(5): 513-518.

• generalized KdV equation
• similarity reduction
• Painleve-I equation
• Painleve-II equation
• cnoidal waves
• dromion-like solution

In this paper, eight types of (1 + 1) -dimensional similarity reductions which contain variable coefficient KdV equation and three good one-dimensional similarity reductions which contain Painleve-I equation and Painleve-II equation, are obtained for the generalized KdV equation in (2+1)-dimensional space arising from the multidimensional isospectral flows associated with the second-order scalar operators by using the direct method. In addition, the cnoidal wave solution and dromion-like solution are also derived by using the reduced nonlinear ordinary differential equations. The (1+1) dromion obtained by Lou [J. Phys, A28 (1995) 7227] and Zhang [Chin. Phys. 9 (2000) 1] is only a special case of our results. Moreover, some properties of the dromion-like solutions are analyzed.

• 出版日期2001-11-15
• 单位大连理工大学