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Article Dans Une Revue Asian Research Journal of Mathematics Année : 2021

Other Families of Rational Solutions to the KPI Equation

Résumé

Aims / Objectives: We present rational solutions to the Kadomtsev-Petviashvili equation (KPI) in terms of polynomials in $x$, $y$ and $t$ depending on several real parameters. We get an infinite hierarchy of rational solutions written as a quotient of a polynomial of degree $2N(N + 1) - 2$ in $x$, $y$ and $t$ by a polynomial of degree $2N(N + 1)$ in $x$, $y$ and $t$, depending on $2N - 2$ real parameters for each positive integer $N$. Place and Duration of Study: Institut de mathématiques de Bourgogne, Université de Bourgogne Franche-Conté between January 2020 and January 2021. Conclusion: We construct explicit expressions of the solutions in the simplest cases $N = 1$ and $N = 2$ and we study the patterns of their modulus in the $(x; y)$ plane for different values of time $t$ and parameters. In particular, in the study of these solutions, we see the appearance not yet observed of three pairs of two peaks in the case of order 2.

Dates et versions

hal-03537324 , version 1 (20-01-2022)

Identifiants

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Pierre Gaillard. Other Families of Rational Solutions to the KPI Equation. Asian Research Journal of Mathematics, 2021, pp.27-34. ⟨10.9734/arjom/2021/v17i630306⟩. ⟨hal-03537324⟩
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