# New Horizons in Mathematical Physics

### Families of Rational Solutions of Order 5 to the KPI Equation Depending on 8 Parameters

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### Author(s)

**P. Gaillard**^{*}

Université de Bourgogne, Institut de mathématiques de Bourgogne, 9 avenue Alain Savary BP 47870 21078 Dijon Cedex, France

### Abstract

equation (KPI). We construct here rational solutions of order 5 as a quotient of 2 polynomials of

degree 60 in x, y and t depending on 8 parameters. The maximum modulus of these solutions at

order 5 is checked as equal to 2(2N + 1)2 = 242. We study their modulus patterns in the plane

(x, y) and their evolution according to time and parameters a1, a2, a3, a4, b1, b2, b3, b4. We get

triangle and ring structures as obtained in the case of the NLS equation.

### Keywords

### References

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