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From Fredholm and Wronskian Representations to Rational Solutions to the KPI Equation Depending on 2N –2 parameters

  • Gaillard, P.
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
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