Peak-height formula for higher-order breathers of the nonlinear Schrödinger equation on nonuniform backgrounds Academic Article uri icon


  • 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.

author list (cited authors)

  • Chin, S. A., Ashour, O. A., Nikolić, S. N., & Belić, M. R.

citation count

  • 6

publication date

  • January 2017