6533b835fe1ef96bd129e92e

RESEARCH PRODUCT

Other 2N− 2 parameters solutions of the NLS equation and 2N+ 1 highest amplitude of the modulus of theNth order AP breather

Pierre Gaillard

subject

Statistics and ProbabilityBreatherMathematical analysisGeneral Physics and AstronomyModulusStatistical and Nonlinear PhysicsConcentric ringNonlinear systemsymbols.namesakeNonlinear Sciences::Exactly Solvable and Integrable SystemsAmplitudeModeling and SimulationsymbolsOrder (group theory)Nonlinear Sciences::Pattern Formation and SolitonsMathematical PhysicsSchrödinger's catMathematics

description

In this paper, we construct new deformations of the Akhmediev-Peregrine (AP) breather of order N (or APN breather) with real parameters. Other families of quasirational solutions of the nonlinear Schrodinger (NLS) equation are obtained. We evaluate the highest amplitude of the modulus of the AP breather of order N; we give the proof that the highest amplitude of the APN breather is equal to . We get new formulas for the solutions of the NLS equation, which are different from these already given in previous works. New solutions for the order 8 and their deformations according to the parameters are explicitly given. We simultaneously get triangular configurations and isolated rings. Moreover, the appearance for certain values of the parameters and of new configurations of concentric rings are underscored.

yearjournalcountryeditionlanguage
2015-03-18Journal of Physics A: Mathematical and Theoretical
https://doi.org/10.1088/1751-8113/48/14/145203