Search results for " 4735Fg"
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From Fredholm and Wronskian representations to rational solutions to the KPI equation depending on 2N − 2 parameters
2017
International audience; 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.
An attempt to classification of the quasi rational solutions to the NLS equation
2015
Based on a representation in terms of determinants of order 2N , an attempt to classification of quasi rational solutions to the one dimensional focusing nonlinear Schrödinger equation (NLS) is given and several conjectures about the structure of the solutions are also formulated. These solutions can be written as a product of an exponential depending on t by a quotient of two polynomials of degree N (N + 1) in x and t depending on 2N −2 parameters. It is remarkable to mention that in this representation, when all parameters are equal to 0, we recover the PN breathers.