The N loop soliton solution of the Vakhnenko equation

An exact N loop soliton solution to the Vakhnenko equation (VE) is found, where N2 is an arbitrary positive integer. The key step in finding this solution is to transform the independent variables in the equation. This leads to a transformed equation for which it is straightforward to find an exact explicit N-soliton solution by using Hirota's method. The exact N loop soliton solution to the VE is then found in implicit form by means of a transformation back to the original independent variables. The shifts that occur when the solitons interact are found. The general results and details of the interaction between solitons are illustrated for the case N = 3.