Nonlinear waves in an anti-Hermitian lattice with cubic nonlinearity

Tombuloglu, S.; Yüce, C.

doi:10.1016/j.cnsns.2019.105106

Cited by 4 publications

(2 citation statements)

References 29 publications

(45 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The system leads to multiple-collision interactions among stable solitons. A study of the nonlinear nonreciprocal dimer in an anti-Hermitian lattice with cubic nonlinearity has been explored recently [66].…”

Section: Introductionmentioning

confidence: 99%

Discrete solitons dynamics in $$\mathscr {PT}$$-symmetric oligomers with complex-valued couplings

Kirikchi

Karjanto

2021

Nonlinear Dyn

View full text Add to dashboard Cite

We consider an array of double oligomers in an optical waveguide device. A mathematical model for the system is the coupled discrete nonlinear Schrödinger (NLS) equations, where the gain-and-loss parameter contributes to the complex-valued linear coupling. The array caters to an optical simulation of the parity-time (PT )-symmetry property between the coupled arms. The system admits fundamental bright discrete soliton solutions. We investigate their existence and spectral stability using perturbation theory analysis. These analytical findings are verified further numerically using the Newton-Raphson method and a standard eigenvalueproblem solver. Our study focuses on two natural discrete modes of the solitons: single-and double-excited-sites, also known as onsite and intersite modes, respectively. Each of these modes acquires three distinct configurations between the dimer arms, i.e., symmetric, asymmetric, and antisymmetric. Although both intersite and onsite discrete solitons are generally unstable, the latter can be stable, depending on the combined values of the propagation constant, horizontal linear coupling coefficient, and gain-loss parameter.

show abstract

Section: Introductionmentioning

confidence: 99%

Discrete solitons dynamics in $$\mathscr {PT}$$-symmetric oligomers with complex-valued couplings

Kirikchi

Karjanto

2021

Nonlinear Dyn

View full text Add to dashboard Cite

show abstract

“…Furthermore, analytical solutions are rare in nonlinear systems. Complete characterization of nonlinear problems can be possible for a simple system such as nonlinear dimer and trimer [37][38][39] but NHSE should be studied for a long lattice to understand the nonlocal effect of distant boundaries. Unfortunately, the complexity of the problem exponentially increases as the nonlinear lattice size is increased.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear non-Hermitian skin effect

Yuce

2021

Preprint

Self Cite

View full text Add to dashboard Cite

Distant boundaries in linear non-Hermitian lattices can dramatically change energy eigenvalues and corresponding eigenstates in a nonlocal way. This effect is known as non-Hermitian skin effect (NHSE). Combining non-Hermitian skin effect with nonlinear effects can give rise to a host of novel phenomenas, which may be used for nonlinear structure designs. Here we study nonlinear non-Hermitian skin effect and explore nonlocal and substantial effects of edges on stationary nonlinear solutions. We show that fractal and continuum bands arise in a long lattice governed by a nonreciprocal discrete nonlinear Schrodinger equation. We show that stationary solutions are localized at the edge in the continuum band. We consider a non-Hermitian Ablowitz-Ladik model and show that nonlinear exceptional point disappears if the lattice is infinitely long.

show abstract