6533b856fe1ef96bd12b2dec

RESEARCH PRODUCT

Families of solutions to the CKP equation with multi-parameters

Pierre Gaillard

subject

Nonlinear Sciences::Exactly Solvable and Integrable Systemswronskiansrational solutions[MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph]4710A-[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP][MATH.MATH-MP] Mathematics [math]/Mathematical Physics [math-ph][MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP]37K10CKP equation PACS numbers : 33Q554735Fg4754BdFredholm determinants

description

We construct solutions to the CKP (cylindrical Kadomtsev-Petviashvili)) equation in terms of Fredholm determinants. We deduce solutions written as a quotient of wronskians of order 2N. These solutions are called solutions of order N ; they depend on 2N − 1 parameters. They can be written as a quotient of 2 polynomials of degree 2N (N + 1) in x, t and 4N (N + 1) in y depending on 2N − 2 parameters. We explicitly construct the expressions up to order 5 and we study the patterns of their modulus in plane (x, y) and their evolution according to time and parameters.

yearjournalcountryeditionlanguage
2020-01-03
https://hal.archives-ouvertes.fr/hal-02427660/document