Solitons in a Hamiltonian $PT$-symmetric coupler

Abstract

We introduce a nonlinear parity-time-symmetric dispersive coupler which admits Hamiltonian and Lagrangian formulations. We show that, in spite of the gain and dissipation, the model has several conservation laws. The system also supports a variety of exact solutions. We focus on exact bright solitons and demonstrate numerically that they are dynamically stable in a wide parameter range and undergo elastic interactions, thus manifesting nearly-integrable dynamics. Physical applications of the introduced model in the theory of Bose-Einstein condensates in nonlinear lattices are discussed.

16 pages, 5 figures; submitted; several corrections made and errors fixed

References in corpus (5)

• Making Sense of Non-Hermitian Hamiltonians
• Unidirectional Nonlinear PT-symmetric Optical Structures
• Hamiltonian formulation of the standard $\mathcal{P}\mathcal{T}$-symmetric nonlinear Schrödinger dimer
• Matter-wave 2D solitons in crossed linear and nonlinear optical lattices
• Nontwist non-Hamiltonian systems

Cited by in corpus (3)

• Constructing Solvable Models of Vector Non-linear Schrodinger Equation with Balanced Loss and Gain via Non-unitary transformation
• Imaginary spin-orbital coupling in parity-time symmetric systems with momentum-dependent gain and loss
• Classical Hamiltonian Systems with Balanced loss and gain