arXiv subjects

H. Susanto

Publications and source records attributed to H. Susanto.

At least 37 records · Page 2Linked to original sources

arXiv2019

Justification of the discrete nonlinear Schrödinger equation from a parametrically driven damped nonlinear Klein-Gordon equation and numerical comparisons

We consider a damped, parametrically driven discrete nonlinear Klein-Gordon equation, that models coupled pendula and micromechanical arrays, among others. To study the equation, one usually uses a small-amplitude wave ansatz, that reduces the equation into a discrete nonlinear Schrödinger equation with damping and parametric drive. Here, we justify the approximation by looking for the error bound with the method of energy estimates. Furthermore, we prove the local and global existence of {solutions to the discrete nonlinear} Schrödinger equation. To illustrate the main results, we consider numerical simulations showing the dynamics of errors made by the discrete nonlinear equation. We consider two types of initial conditions, with one of them being a discrete soliton of the nonlinear Schrödinger equation, that is expectedly approximate discrete breathers of the nonlinear Klein-Gordon equation.

nlin.PS↗

arXiv2019

Snakes in square, honeycomb, and triangular lattices

We present a study of time-independent solutions of the two-dimensional discrete Allen-Cahn equation with cubic and quintic nonlinearity. Three different types of lattices are considered, i.e., square, honeycomb, and triangular lattices. The equation admits uniform and localised states. We can obtain localised solutions by combining two different states of uniform solutions, which can develop a snaking structure in the bifurcation diagrams. We find that the complexity and width of the snaking diagrams depend on the number of "patch interfaces" admitted by the lattice systems. We introduce an active-cell approximation to analyse the saddle-node bifurcation and stabilities of the corresponding solutions along the snaking curves. Numerical simulations show that the active-cell approximation gives good agreement for all of the lattice types when the coupling is weak. We also consider planar fronts that support our hypothesis on the relation between the complexity of a bifurcation diagram and the number of interface of its corresponding solutions.

nlin.PS↗

arXiv2019

Soliton and breather splitting on star graphs from tricrystal Josephson junctions

We consider the interactions of traveling localized wave solutions with a vertex in a star graph domain that describes multiple Josephson junctions with a common/branch point (i.e., tricrystal junctions). The system is modeled by the sine-Gordon equation. The vertex is represented by boundary conditions that are determined by the continuity of the magnetic field and vanishing total fluxes. When one considers small-amplitude breather solutions, the system can be reduced into the nonlinear Schrödinger equation posed on a star graph. Using the equation, we show that a high-velocity incoming soliton is split into a transmitted component and a reflected one. The transmission is shown to be in good agreement with the transmission rate of plane waves in the linear Schrödinger equation on the same graph (i.e., a quantum graph). In the context of the sine-Gordon equation, small-amplitude breathers show similar qualitative behaviors, while large-amplitude ones produce complex dynamics.

nlin.PS↗

arXiv2019

Solitons in a chain of charge-parity-symmetric dimers

We consider an array of dual-core waveguides, which represent an optical realization of a chain of dimers, with an active (gain-loss) coupling between the cores, opposite signs of discrete diffraction in the parallel arrays, and a phase-velocity mismatch between them (which is necessary for the stability of the system). The array provides an optical emulation of the charge-parity ($\mathcal{CP}$) symmetry. The addition of the intracore cubic nonlinearity gives rise to several species of fundamental discrete solitons, which exist in continuous families, although the system is non-Hermitian. The existence and stability of the soliton families are explored by means of analytical and numerical methods. An asymptotic analysis is presented for the case of weak intersite coupling (i.e., near the anticontinuum limit), as well as weak coupling between cores in each dimer. Several families of fundamental discrete solitons are found in the semi-infinite gap of the system's spectrum, that have no counterparts in the continuum limit, as well as a branch which belongs to the finite band gap and carries over into a family of stable gap solitons in that limit. One branch develops an oscillatory instability above a critical strength of the intersite coupling, others being stable in their entire existence regions. Unlike solitons in conservative lattices, which are controlled solely by the strength of the intersite coupling, here fundamental-soliton families have several control parameters, one of which, viz., the coefficient of the intercore coupling in the active host medium, may be readily adjusted in the experiment by varying the gain applied to the medium.

nlin.PS↗

arXiv2019

Networks with point like nonlinearities

We study static nonlinear waves in networks described by a nonlinear Schrodinger equation with point-like nonlinearities on metric graphs. Explicit solutions fulfilling vertex boundary conditions are obtained. Spontaneous symmetry breaking caused by bifurcations is found.

nlin.PS↗

arXiv2019

Calculated threshold of supratransmission phenomena in waveguide arrays with saturable nonlinearity

In this work, we consider a semi-infinite discrete nonlinear Schrödinger equation with saturable nonlinearity driven at one edge by a driving force. The equation models the dynamics of coupled photorefractive waveguide arrays. It has been reported that when the frequency of the driving force is in the forbidden band, energy can be transmitted along the lattices provided that the driving amplitude is above a critical value. This nonlinear tunneling is called supratransmission. Here, we explain the source of supratransmission using geometric illustrations. Approximations to the critical amplitude for supratransmission are presented as well.

physics.optics↗

arXiv2018

Quantum dynamics of PT-symmetrically kicked particle confined in a 1D box

We study quantum particle dynamics in a box and driven by PT-symmetric, delta-kicking complex potential. Such dynamical characteristics as the average kinetic energy as function of time and quasi-energy at different values of the kicking parameters. Breaking of the PT-symmetry at certain values of the non-Hermitian kicking parameter is shown. Experimental realization of the model is also discussed.

quant-ph↗

arXiv2018

Snakes and ghosts in a parity-time-symmetric chain of dimers

We consider linearly coupled discrete nonlinear Schrödinger equations with gain and loss terms and with a cubic-quintic nonlinearity. The system models a parity-time ($\cal{PT}$)-symmetric coupler composed by a chain of dimers. Particularly we study site-centered and bond-centered spatially-localized solutions and present that each solution has a symmetric and antisymmetric configuration between the arms. When a parameter is varied, the resulting bifurcation diagrams for the existence of standing localized solutions have a snaking behaviour. The critical gain/loss coefficient above which the $\cal{PT}-$symmetry is broken corresponds to the condition when bifurcation diagrams of symmetric and antisymmetric states merge. Past the symmetry breaking, the system no longer has time-independent states. Nevertheless, equilibrium solutions can be analytically continued by defining a dual equation that leads to so-called ghost states associated with growth or decay, that are also identified and examined here. We show that ghost localized states also exhibit snaking bifurcation diagrams. We analyse the width of the snaking region and provide asymptotic approximations in the limit of strong and weak coupling where good agreement is obtained.

nlin.PS↗

arXiv2017

Gain-loss-driven travelling waves in PT-symmetric nonlinear metamaterials

In this work we investigate a one-dimensional parity-time (PT)-symmetric magnetic metamaterial consisting of split-ring dimers having gain or loss. Employing a Melnikov analysis we study the existence of localized travelling waves, i.e. homoclinic or heteroclinic solutions. We find conditions under which the homoclinic or heteroclinic orbits persist. Our analytical results are found to be in good agreement with direct numerical computations. For the particular nonlinearity admitting travelling kinks, numerically we observe homoclinic snaking in the bifurcation diagram. The Melnikov analysis yields a good approximation to one of the boundaries of the snaking profile.

nlin.PS↗

arXiv2017

Newton's method's basins of attraction revisited

In this paper, we revisit the chaotic number of iterations needed by Newton's method to converge to a root. Here, we consider a simple modified Newton method depending on a parameter. It is demonstrated using polynomiography that even in the simple algorithm the presence and the position of the convergent regions, i.e. regions where the method converges nicely to a root, can be complicatedly a function of the parameter.

math.NA↗

arXiv2017

Exploiting bifurcations in waveguide arrays for light detectors

An array of a finite number waveguides, driven laterally by injecting light at the outer waveguides, is considered. The array is modeled by a discrete nonlinear Schrödinger equation. It has been shown [Phys. Rev. Lett. 94, 243902 (2005)] that, when the injected light is in the proximity of a bifurcation point, such a system can be sensitive to small disturbances, making it possible to act as a light detector. Here, the optimum intensity of the injected light is discussed, and an analytical approximation is presented.

nlin.PS↗

arXiv2016

The stationary sine-Gordon equation on metric graphs: Exact analytical solutions for simple topologies

We consider the stationary sine-Gordon equation on metric graphs with simple topologies. The vertex boundary conditions are provided by flux conservation and matching of derivatives at the star graph vertex. Exact analytical solutions are obtained. It is shown that the method can be extended for tree and other simple graph topologies. Applications of the obtained results to branched planar Josephson junctions and Josephson junctions with tricrystal boundaries are discussed.

nlin.SI↗

arXiv2016

Interactions of bright and dark solitons with localized $\mathcal{PT}$-symmetric potentials

We study collisions of moving nonlinear-Schrödinger solitons with a $\mathcal{PT}$-symmetric dipole embedded into the one-dimensional self-focusing or defocusing medium. Accurate analytical results are produced for bright solitons, and, in a more qualitative form, for dark ones. In the former case, an essential aspect of the approximation is that it must take into regard the intrinsic chirp of the soliton, thus going beyond the framework of the simplest quasi-particle description of the soliton's dynamics. Critical velocities separating reflection and transmission of the incident bright solitons are found by means of numerical simulations, and in the approximate semi-analytical form. An exact solution for the dark soliton pinned by the complex $\mathcal{PT}$-symmetric dipole is produced too.

nlin.PS↗

arXiv2016

Superfluid flow past an obstacle in annular Bose--Einstein condensates

We investigate the flow of a one-dimensional nonlinear Schrodinger model with periodic boundary conditions past an obstacle, motivated by recent experiments with Bose--Einstein condensates in ring traps. Above certain rotation velocities, localized solutions with a nontrivial phase profile appear. In striking difference from the infinite domain, in this case there are many critical velocities. At each critical velocity, the steady flow solutions disappear in a saddle-center bifurcation. These interconnected branches of the bifurcation diagram lead to additions of circulation quanta to the phase of the associated solution. This, in turn, relates to the manifestation of persistent current in numerous recent experimental and theoretical works, the connections to which we touch upon. The complex dynamics of the identified waveforms and the instability of unstable solution branches are demonstrated.

cond-mat.quant-gas↗

arXiv2016

The spin-flip model of spin-polarized vertical-cavity surface-emitting lasers: asymptotic analysis, numerics, and experiments

The spin-flip model describing optically pumped spin-polarized vertical-cavity surface-emitting lasers is considered. The steady-state solutions of the model for elliptically-polarised fields are studied. Asymptotic analysis for the existence and stability of the steady-state solutions is developed, particularly in the presence of pump polarisation ellipticity. The expansion is with respect to small parameters representing the ellipticity and the difference between the total pump power and the lasing threshold. The analytical results are then confirmed numerically, where it is obtained that generally one of the steady-state solutions is stable while the other is not. The theoretical results are shown to be in qualitative agreement with the experiments.

physics.optics↗

arXiv2014

Dynamics of generalized PT-symmetric dimers with time periodic gain-loss

A Parity-Time (PT)-symmetric system with periodically varying-in-time gain and loss modeled by two coupled Schrodinger equations (dimer) is studied. It is shown that the problem can be reduced to a perturbed pendulum-like equation. This is done by finding two constants of motion. Firstly, a generalized problem using Melnikov type analysis and topological degree arguments is studied for showing the existence of periodic (libration), shift periodic (rotation), and chaotic solutions. Then these general results are applied to the PT-symmetric dimer. It is interestingly shown that if a sufficient condition is satisfied, then rotation modes, which do not exist in the dimer with constant gain-loss, will persist. An approximate threshold for PT-broken phase corresponding to the disappearance of bounded solutions is also presented. Numerical study is presented accompanying the analytical results.

nlin.PS↗

arXiv2013

On the integrability of PT-symmetric dimers

The coupled discrete linear and Kerr nonlinear Schrodinger equations with gain and loss describing transport on dimers with parity-time PT symmetric potentials are considered. The model is relevant among others to experiments in optical couplers and proposals on Bose-Einstein condensates in PT symmetric double-well potentials. It is known that the models are integrable. Here, the integrability is exploited further to construct the phase-portraits of the system. A pendulum equation with a linear potential and a constant force for the phase-difference between the fields is obtained, which explains the presence of unbounded solutions above a critical threshold parameter. The behaviour of all solutions of the system, including changes in the topological structure of the phase-plane, is then discussed.

physics.optics↗

arXiv2013

An instability criterion for nonlinear standing waves on nonzero backgrounds

A nonlinear Schrödinger equation with repulsive (defocusing) nonlinearity is considered. As an example, a system with a spatially varying coefficient of the nonlinear term is studied. The nonlinearity is chosen to be repelling except on a finite interval. Localized standing wave solutions on a non-zero background, e.g., dark solitons trapped by the inhomogeneity, are identified and studied. A novel instability criterion for such states is established through a topological argument. This allows instability to be determined quickly in many cases by considering simple geometric properties of the standing waves as viewed in the composite phase plane. Numerical calculations accompany the analytical results.

nlin.PS↗