title: Peak-height formula for higher-order breathers of the nonlinear Schrödinger equation on nonuniform backgrounds.
abstract: Given any background (or seed) solution of the nonlinear Schrödinger equation, the Darboux transformation can be used to generate higher-order breathers with much greater peak intensities. In this work, we use the Darboux transformation to prove, in a unified manner and without knowing the analytical form of the background solution, that the peak height of a high-order breather is just a sum of peak heights of first-order breathers plus that of the background, irrespective of the specific choice of the background. Detailed results are verified for breathers on a cnoidal background. Generalizations to more extended nonlinear Schrödinger equations, such as the Hirota equation, are indicated.
authors.affiliation: Department of Physics and Astronomy, Texas A&M University, College Station, Texas 77843, USA.
authors.forename: Siu A
authors.initials: SA
authors.lastname: Chin
authors.affiliation: Department of Physics and Astronomy, Texas A&M University, College Station, Texas 77843, USA.|Science Program, Texas A&M University at Qatar, P.O. Box 23874 Doha, Qatar.
authors.forename: Omar A
authors.initials: OA
authors.lastname: Ashour
authors.affiliation: Science Program, Texas A&M University at Qatar, P.O. Box 23874 Doha, Qatar.|Institute of Physics, University of Belgrade, Pregrevica 118, 11080 Belgrade, Serbia.
authors.forename: Stanko N
authors.initials: SN
authors.lastname: Nikolić
authors.affiliation: Science Program, Texas A&M University at Qatar, P.O. Box 23874 Doha, Qatar.
authors.forename: Milivoj R
authors.initials: MR
authors.lastname: Belić