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Article Dans Une Revue Fundamental Journal of Mathematics and Applications Année : 2019

Rational Solutions to the Boussinesq Equation

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Résumé

Rational solutions to the Boussinesq equation are constructed as a quotient of two polynomials in xx and tt. For each positive integer NN, the numerator is a polynomial of degree N(N+1)−2N(N+1)−2 in xx and tt, while the denominator is a polynomial of degree N(N+1)N(N+1) in xx and tt. So we obtain a hierarchy of rational solutions depending on an integer NN called the order of the solution. We construct explicit expressions of these rational solutions for N=1N=1 to 44.

Dates et versions

hal-02194575 , version 1 (25-07-2019)

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Pierre Gaillard. Rational Solutions to the Boussinesq Equation. Fundamental Journal of Mathematics and Applications, 2019, 2 (1), pp.1-4. ⟨10.33401/fujma.512333⟩. ⟨hal-02194575⟩
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