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From Fredholm and Wronskian Representations to Rational Solutions to the KPI Equation Depending on 2N –2 parameters
-
- P. Gaillard
- We have already constructed solutions to the Kadomtsev-Petviashvili equation (KPI) in terms of Fredholm determinants and wronskians of order 2N. These solutions have been called solutions of order N and they depend on 2N −1 parameters. We construct here N-order rational solutions. We prove that they can be written as a quotient of 2 polynomials of degree 2N(N +1) in x, y and t 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.
- Select Volume / Issue:
- Year:
- 2017
- Type of Publication:
- Article
- Keywords:
- Kadomtsev Petviashvili Equation; Fredholm Determinants; Wronskians; Rogue Waves; Lumps
- Journal:
- IJASM
- Volume:
- 4
- Number:
- 3
- Pages:
- 60-70
- Month:
- May
- ISSN:
- 2394-2894