Blow-up solutions for L2 supercritical gKdV equations with exactly k blow-up points

In this paper we consider the slightly L-2-supercritical gKdV equations partial derivative(t)u + (u(xx) + u vertical bar u vertical bar(p-1))(x) = 0, with the nonlinearity 5 < p < 5 + epsilon and 0 < epsilon << 1. In the previous work of the author, we know that there exists a stable self-similar blow-up dynamics for slightly L-2-supercritical gKdV equations. Such solutions can be viewed as solutions with a single blow-up point. In this paper we will prove the existence of solutions with multiple blow-up points, and give a description of the formation of the singularity near the blow-up time.