Hyperelliptic function solutions with finite genus ������ of coupled nonlinear differential equations*

Abstract

In this paper, using the properties of hyperelliptic σ-and ℘-functions, ℘ µν := ∂ µ ∂ ν log σ, we propose an algorithm to obtain particular solutions of the coupled nonlinear differential equations, such as a general (2+1)-dimensional breaking soliton equation and static Veselov-Novikov(SVN) equation, the solutions of which can be expressed in terms of the hyperelliptic Kleinian functions for a given curve y 2 = f (x) of (2g+1)-and (2g+2)-degree with genus G . In particular, owing to the idea of CK direct method, the algorithm can generate a series of new forms of hyperelliptic function solutions with the same genus G .