  The Camassa-Holm-Kadomtsev-Petviashvili-I equation (CH-KP-I) is a two
dimensional generalization of the Camassa-Holm equation (CH). In this paper, we
prove transverse instability of the line solitary waves under periodic
transverse perturbations. The proof is based on the framework of the paper
written by Rousset and Tzvetkov. Due to the high nonlinearity, our proof
requires necessary modification. Specifically, we first establish the linear
instability of the line solitary waves. Then through an approximation
procedure, we prove that the linear effect actually dominates the nonlinear
behavior.
