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RESEARCH PRODUCT

Fredholm and wronskian representations of solutions to the Johnson equation and the third order case

subject

description

We construct solutions to the Johnson equation (J) by means of Fred-holm determinants first, then by means of wronskians of order 2N giving solutions of order N depending on 2N − 1 parameters. We obtain N order rational solutions which can be written as a quotient of two polynomials of degree 2N (N + 1) in x, t and 4N (N + 1) in y depending on 2N − 2 parameters. This method gives an infinite hierarchy of solutions to the Johnson equation. In particular, rational solutions are obtained. The solutions of order 3 with 4 parameters are constructed and studied in detail by means of their modulus in the (x, y) plane in function of time t and parameters a1, a2, b1, b2.