Rational solutions to the Johnson equation of order N depending on 2N − 2 parameters

Abstract : We construct rational solutions of order N depending on 2N − 2 parameters. They can be written as a quotient of 2 polynomials of degree 2N (N + 1) in x, t and 4N (N + 1) in y depending on 2N − 2 parameters. We explicitly construct the expressions of the rational solutions of order 4 depending on 6 real parameters and we study the patterns of their modulus in the plane (x, y) and their evolution according to time and parameters a1, a2, a3, b1, b2, b3.
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https://hal.archives-ouvertes.fr/hal-02111571
Contributor : Pierre Gaillard <>
Submitted on : Friday, April 26, 2019 - 10:06:05 AM
Last modification on : Thursday, May 2, 2019 - 1:30:18 AM

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Pierre Gaillard. Rational solutions to the Johnson equation of order N depending on 2N − 2 parameters. 2019. ⟨hal-02111571⟩

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