Abundant new explicit exact soliton-like solutions and Painleve test for the generalized Burgers equation in (2+1)-dimensional space

作者：Yan ZY^*

来源：Communications in Theoretical Physics, 2001, 36(2): 135-138.

• generalized Burgers equation
• Backlund transformation
• exact solution
• Painleve test

We obtain Backlund transformation and some new kink-like solitary wave solutions for the generalized Burgers equation in (2+1)-dimensional space, u(t) + 1/2 (u partial derivative (-1)(y)u(x))(x) - u(xx) = 0, by using the extended homogeneous balance method. As is well known, the introduction of the concept of dromions (the exponentially localized solutions in (2+1)dimensional space) has triggered renewed interest in (2+1) -dimensional soliton systems. The solutions obtained are used to show that the variable u(x) admits exponentially localized solutions rather than the physical Bold u(x,y,t) itself. In addition, it is shown that the equation passes Painleve test.

• 出版日期2001-8-15
• 单位大连理工大学