Abstract

Breathers are coherent structures in nonlinear dispersive media that are localized disturbances in space (or time) and periodic in time (or space) in a comoving reference frame. They consist of two distinct time scales: one associated with propagation and the other associated with internal oscillations, exhibiting rich mathematical properties due to the complexity of their two-phase configuration. Breathers are ubiquitous excitations in many physical systems, including large ocean waves, optics, lattices, and materials. Theoretical constructions of the exact breather solutions have focused on the nonlinear superposition of solitons and cnoidal waves in weakly nonlinear, completely integrable systems. However, experimental confirmation of this superposition and its applicability in fully nonlinear systems are lacking. In this work, breathers of both bright and dark types in a physical two-Stokes core-annular flow system are investigated experimentally. Single breathers and breather interactions are realized to be the result of the nonlinear superposition of locally created solitary waves and locally created cnoidal-like waves. Moreover, the exact breather solutions to the two-Stokes interfacial wave model are obtained by numerical computations of a space-time boundary value problem. The experimental measurements are found to quantitatively agree with the exact solutions. Co-Authors: Sathyanarayanan Chandramouli (Florida State University), Mark Hoefer (University of Colorado Boulder)