The following study is part of a research program of rational solutions of the hierarchy of the nonlinear Schrodinger equation. Here, we are interested in the equation of order 7 and we highlight particular solutions providing the first orders of rogue waves not yet found.
Open access
Research Article10.9734/ajarr/2024/v18i7700
This study is part of a research program of rational solutions of the hierarchy of the nonlinear Schrodinger equation. Here, we are interested in the equation of order 5 and we construct explicitly the first orders of rogue waves which were not yet found. In particular, quasi rat...
Open access
Research Article10.9734/ajr2p/2024/v8i2164
Quasi-rational solutions to the Lakshmanan Porsezian Daniel equation are presented. We construct explicit expressions of these solutions for the first orders depending on real parameters. We study the patterns of these configurations in the (x, t) plane in function of the differe...
Open access
Research Article10.9734/ajarr/2022/v16i330463
Aims / Objectives: We present rational solutions to the Kadomtsev-Petviashvili equation (KPI) in terms of polynomials in x, y and t depending on several real parameters. We get an infinite hierarchy of rational solutions written as a quotient of a polynomial of degree 2N(N + 1) -...
Open access
Research Article10.9734/arjom/2021/v17i630306
We construct multi-parametric rational solutions to the KdV equation. For this, we use solutions in terms of exponentials depending on several parameters and take a limit when one of these parameters goes to 0. Here we present degenerate rational solutions and give a result witho...
Open access
Research Article10.9734/ajr2p/2021/v4i330143
The twelfth Peregrine breather (P12 breather) solution to the focusing one dimensional nonlinear Schr¨odinger equation (NLS) with its twenty two real parameters deformations solutions to the NLS equation are explicitly constructed here. New families of quasi-rational solutions of...
Open access
Research Article10.9734/AIR/2016/25636
Aims/ The structure of the solutions to the one dimensional focusing nonlinear Schr¨odinger equation (NLS) for the order N in terms of quasi rational functions is given here. We first give the proof that the solutions can be expressed as a ratio of two wronskians of order 2N and...
Open access
Research Article10.9734/AIR/2015/16827