Stability of soliton families in nonlinear Schroedinger equations with non-parity-time-symmetric complex potentials

Jianke Yang; Sean Nixon

doi:10.1016/j.physleta.2016.09.023

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arXiv · 1605.02259

Stability of soliton families in nonlinear Schroedinger equations with non-parity-time-symmetric complex potentials

Jianke Yang·Sean Nixon

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Abstract

Stability of soliton families in one-dimensional nonlinear Schroedinger equations with non-parity-time (PT)-symmetric complex potentials is investigated numerically. It is shown that these solitons can be linearly stable in a wide range of parameter values both below and above phase transition. In addition, a pseudo-Hamiltonian-Hopf bifurcation is revealed, where pairs of purely-imaginary eigenvalues in the linear-stability spectra of solitons collide and bifurcate off the imaginary axis, creating oscillatory instability, which resembles Hamiltonian-Hopf bifurcations of solitons in Hamiltonian systems even though the present system is dissipative and non-Hamiltonian. The most important numerical finding is that, eigenvalues of linear-stability operators of these solitons appear in quartets $(λ, -λ, λ^*, -λ^*)$, similar to conservative systems and PT-symmetric systems. This quartet eigenvalue symmetry is very surprising for non-PT-symmetric systems, and it has far-reaching consequences on the stability behaviors of solitons.

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Jianke Yang, Sean Nixon. 2016-05-08. Stability of soliton families in nonlinear Schroedinger equations with non-parity-time-symmetric complex potentials. https://doi.org/10.1016/j.physleta.2016.09.023

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