A Bilinear N-Soliton Formula for the KP Equation

Abstract

We consider the new derivations of the bilinear N-soliton solutions for the KP (two dimensional KdV) equation which utilize the Jacobi formula of the matrix algebra. The periodic waves of explode-decay type are shown to be derived easily in the present approach. It is shown that physically important several other nonlinear equations can be cast into our present form of “four-operators” bilinear equation.