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

Abstract : 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.
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Contributor : Pierre Gaillard <>
Submitted on : Saturday, February 9, 2019 - 3:55:56 PM
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Pierre Gaillard. Fredholm and wronskian representations of solutions to the Johnson equation and the third order case. 2019. ⟨hal-02012908⟩

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