Bilinear equations and new multi-soliton solution for the modified Camassa–Holm equation

The bilinear equations, which directly derive the modified Camassa–Holm equation, are given from the reduction of the extended KP hierarchy with negative flow. As a byproduct, the general NN-soliton solution in the parametric form to the modified Camassa–Holm equation is obtained from the tau functions of the extended KP hierarchy in the form of Gram-type determinant.