Maximal Intensity Higher-Order Breathers of the Nonlinear Schrödinger Equation on Different Backgrounds

Abstract

In this work, we present fully periodic breathers of the nonlinear Schrodinger equation (NLSE) on both constant and elliptical dn-function backgrounds. The breathers can be generated under two conditions 1) the periods of the constituent breathers of the higher-order structures must be commensurate with each other; and 2) the period of the constituent first order breather must be commensurate with the period of the background. Breathers on constant backgrounds of arbitrary order can be generated numerically using a fully systematic procedure, pointing to the possibility of generating them experimentally using frequency combs. The peak height formula is presented and used to prove that these families of breathers are of maximal intensity.