The Johnson equation, Fredholm and Wronskian representations of solutions, and the case of order three
type: Item
instance of: scholarly article
title: The Johnson equation, Fredholm and Wronskian representations of solutions, and the case of order three
zbMATH Open document ID: 1412.76018
DOI: 10.1155/2018/1642139
author: Pierre Gaillard
published in: Advances in Mathematical Physics
publication date: 2018-12-11T00:00:00Z
review text: Summary: We construct solutions to the Johnson equation (J) first by means of Fredholm determinants and then by means of Wronskians of order \(2 N\) giving solutions of order \(N\) depending on \(2 N - 1\) parameters. We obtain \(N\) order rational solutions that can be written as a quotient of two polynomials of degree \(2 N(N + 1)\) in \(x\), \(t\) and \(4 N(N + 1)\) in \(y\) depending on \(2 N - 2\) 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 \(a_1\), \(a_2\), \(b_1\), and \(b_2\).
Mathematics Subject Classification ID: 76B15
Mathematics Subject Classification ID: 35Q53
zbMATH DE Number: 6991926
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2018/1642139
OpenAlex ID: W2885925517
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Wikidata QID: Q129428650
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description: scientific article; zbMATH DE number 6991926