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

Pierre Gaillard

Advances in Mathematical Physics, 2018, vol. 2018, 1-18

Abstract:

We construct solutions to the Johnson equation (J) first by means of Fredholm determinants and then by means of Wronskians of order giving solutions of order depending on parameters. We obtain order rational solutions that can be written as a quotient of two polynomials of degree in , and in depending on parameters. This method gives an infinite hierarchy of solutions to the Johnson equation. In particular, rational solutions are obtained. The solutions of order with parameters are constructed and studied in detail by means of their modulus in the plane in function of time and parameters , , , and .

Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlamp:1642139

DOI: 10.1155/2018/1642139

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