Solution of ODE u＂ ＋ p（u）（u＇）^2＋ q（u） = 0 and Applications to Classifications of All Single Travelling Wave Solutions to Some Nonlinear Mathematical Physics Equations

Under the travelling wave transformation, some nonlinear partial differential equations such as Camassa-Holm equation, High-order KdV equation, etc., are reduced to an integrable ODE expressed by u＂ ＋p（u）（u＇）^2 ＋ q（u） = 0 whose generai solution can be given. Furthermore, combining complete discrimination system for polynomiai, the classifications of all single travelling wave solutions to these equations are obtained. The equation u＂＋p（u）（u＇）^2＋q（u） = 0 includes the equation （u＇）^2 = f（u） as a special case, so the proposed method can be also applied to a large number of nonlinear equations. These complete results cannot be obtained by any indirect method.     

具有色散系数的（2＋1）维非线性Schroedinger方程的有理解和空间孤子

非线性Schroedinger方程是物理学中具有广泛应用的非线性模型之一．本文采用相似变换,将具有色散系数的（2＋1）维非线性Schrioedinger方程简化成熟知的Schroedinger方程,进而得到原方程的有理解和一些空间孤子．