The Johnson Equation, Fredholm and Wronskian Representations of Solutions, and the Case of Order Three

Pierre Gaillard

Advances in Mathematical Physics, 2018, vol. 2018, issue 1

Abstract: We construct solutions to the Johnson equation (J) first by means of Fredholm determinants and then by means of Wronskians of order 2N giving solutions of order N depending on 2N − 1 parameters. We obtain N order rational solutions that 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, and b2.

Date: 2018
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https://doi.org/10.1155/2018/1642139

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlamp:v:2018:y:2018:i:1:n:1642139

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