6533b82cfe1ef96bd128f13a

RESEARCH PRODUCT

An extended Darboux transformation to get families of solutions to the KPI equation

Pierre Gaillard

subject

KPI equationwronskiansrational solutions[MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP]Darboux transformation

description

By means of a Darboux transform with particular generating function solutions to the Kadomtsev-Petviashvili equation (KPI) are constructed. We give a method that provides different types of solutions in terms of particular determinants of order N. For any order, these solutions depend of the degree of summation and the degree of derivation of the generating functions. We study the patterns of their modulus in the plane (x, y) and their evolution according time and parameters.

yearjournalcountryeditionlanguage
2023-01-01
https://hal.science/hal-04014108