We construct solutions to the Johnson equation in terms of Fredholm determinants. We deduce solutions written as a quotient of wronskians of order 2N. These solutions are called solutions of order N; they depend on 2N - 1 parameters. They can be written as a quotient of 2 polynomials of degree 2N(N + 1) in x, t and 4N(N + 1) in y depending on 2N - 2 parameters. We explicitly construct the expressions up to order 5 and we study the patterns of their modulus in plane (x, y) and their evolution according to time and parameters.