Isaac Towers

Stable (2+1)-dimensional solitons in a layered medium with sign-alternating Kerr nonlinearity

Transverse beam propagation is considered in a layered structure in which Kerr nonlinearity alternates between self-focusing and self-defocusing, which makes it possible to prevent collapse. A structure composed of alternating self-focusing layers with strongly different values of the Kerr coefficient is considered too. By means of both a variational approximation (which is implemented in a completely analytical form, including the stability analysis) and direct simulations, it is demonstrated that stable quasi-stationary (2+1)-dimensional soliton beams exist in these media (direct simulations demonstrate stable propagation over a distance exceeding 100 diffraction lengths of the beam). Quasi-stationary cylindrical solitons with intrinsic vorticity exist too, but they all are unstable, splitting into separating zero-vorticity beams.

Stability of spinning ring solitons of the cubic–quintic nonlinear Schrödinger equation

Abstract We investigate stability of (2+1)-dimensional ring solitons of the nonlinear Schrodinger equation with focusing cubic and defocusing quintic nonlinearities. Computing eigenvalues of the linearised equation, we show that rings with spin (topological charge) s=1 and s=2 are linearly stable, provided that they are very broad. The stability regions occupy, respectively, 9% and 8% of the corresponding existence regions. These results finally resolve a controversial stability issue for this class of models.

Unified semiclassical approximation for Bose-Einstein condensates: Application to a BEC in an optical potential

We present semiclassical descriptions of Bose-Einstein condensates for configurations with spatial symmetry, e.g., cylindrical symmetry, and without any symmetry. The description of the cylindrical case is quasi-one-dimensional (Q1D), in the sense that one only needs to solve an effective 1D nonlinear Schroedinger equation, but the solution incorporates 3D aspects of the problem, as a result of which the 1D equation is supplemented by a noncanonical (quartic) normalization condition. The solution in classically allowed regions is matched onto that in classically forbidden regions by a connection formula that properly accounts for the nonlinear mean-field interaction. Special cases for vortex solutions are treated too. Comparisons of the Q1D solution with the full 3D and Thomas-Fermi ones are presented, and conditions for the applicability of the effective low-dimensional equations are obtained.

Soliton multistability as a result of double-resonance wave mixing in chi((2)) media.

We investigate analytically and numerically the existence and stability properties of three-wave solitons resulting from double-resonance (type I plus type II) parametric interaction in a purely quadratic nonlinear medium. The existence of a family of stable solitons for the double-resonance model is demonstrated in a broad parameter range. Moreover, these solitons are shown to exhibit multistability, a feature that is potentially useful for optical switching applications. Finally, we find and present a novel family of quasi solitons.

Bistability of flame propagation in a model with competing exothermic reactions

We investigate a diffusional-thermal model with two-step competitive exothermic reactions for premixed combustion wave propagation in one spatial dimension under adiabatic conditions. A criterion based on the crossover temperature notion was used to qualitatively predict the region in the space of parameters where three travelling combustion wave solutions coexist, which are further studied via numerical means. It is demonstrated that under certain conditions the flame speed is an ‘S’-shaped function of parameters. The fast branch is either stable or is partly stable and exhibits the Andronov–Hopf (AH) bifurcation before the turning point is reached. The mid-branch is completely unstable. The slow solution branch is either unstable or partly stable and exhibits a single or a pair of AH bifurcations. The AH bifurcations are shown to be supercritical giving rise to stable pulsating waves. Bistability and hysteresis phenomena are also demonstrated.

A model for multiple isothermal circumstellar dust shells

We have extended our previously described single and double-shell isothermal circumstellar dust shell models to the case of an arbitrary number of independent isothermal shells. We envisage that this model, the code for which is available on-line, may be useful in three ways: (i) as a tool for the quick representation of the spectrum of dust enshrouded objects, (ii) as an initial guide to the choice of parameters to be used in more sophisticated models and (iii) as a teaching aid for a simple application of radiative transfer theory. For illustrative purposes this model has been used to represent the spectral energy distribution of two evolved objects with optically thick circumstellar dust shells, the post asymptotic giant branch (post-AGB) star IRAS 22036+5306 and the proto-planetary nebula (PPN) M1-92. Both of these objects have very broad spectral energy distributions, their flat distributions having proven difficult to model in the past. The satisfactory fit of the models supports the considerable evidence that some evolved objects in particular, may have multiple discrete circumstellar dust shells, possibly ejected from the central star at different epochs and with different grain compositions. In addition, the isothermal nature of the models suggests the possibility that these shells may be quite limited in their temperature range and physical extent.

Impacts of Biotic Resource Enrichment on a Predator–Prey Population

The environmental carrying capacity is usually assumed to be fixed quantity in the classical predator–prey population growth models. However, this assumption is not realistic as the environment generally varies with time. In a bid for greater realism, functional forms of carrying capacities have been widely applied to describe varying environments. Modelling carrying capacity as a state variable serves as another approach to capture the dynamical behavior between population and its environment. The proposed modified predator–prey model is based on the ratio-dependent models that have been utilized in the study of food chains. Using a simple non-linear system, the proposed model can be linked to an intra-guild predation model in which predator and prey share the same resource. Distinct from other models, we formulate the carrying capacity proportional to a biotic resource and both predator and prey species can directly alter the amount of resource available by interacting with it. Bifurcation and numerical analyses are presented to illustrate the system’s dynamical behavior. Taking the enrichment parameter of the resource as the bifurcation parameter, a Hopf bifurcation is found for some parameter ranges, which generate solutions that posses limit cycle behavior.

Multistability and homoclinic clamping in nonlinear quadratic distributed feedback systems

Summary form only given. After successful demonstration of cascading phenomena and solitary waves in quadratic media, we are challenged to fully understand and exploit second-harmonic generation in periodic media. These /spl chi//sup (2)/ nonlinear distributed feedback systems (NLDFBSs) exhibit noteworthy phenomena such as bistability and gap solitons. We analyze the CW field dynamics sustained by different cascading limits in quadratic NLDFBSs. Our analytical approach reveals the existence of spatial instability effects responsible for novel features such as strong frustration (clamping) of NLDFBS transmissivity in the limit of large nonlinear phase mismatch, and the possibility of pronounced multibranch multistable behavior when operating close to nonlinear phase-matching.

Two-color bright solitons in a three-level atomic system in the cascade configuration

We investigate two-component spatial optical solitons in a cascaded three-level atomic system. We derive an existence curve in the parameter space of power and spatial widths that reveals the existence of a plethora of coupled solitons. These solitons can exist with two different frequencies and also with two different widths. Our analytical results have been verified by direct numerical simulations. Stability analysis confirms that these solitons are stable.

Quadratic solitons resulting from double- resonance wave mixing

The existence and stability of three-wave solitons, both (1+1) and (2+1) dimensional, that result from a double-resonance (type I plus type II) parametric interaction in a purely quadratic nonlinear medium are investigated. We demonstrate the existence of a family of stable solitons for a broad parameter range in the double-resonance model. Further, these solitons exhibit multistability, a property that is potentially useful for optical switching applications. We introduce a way to measure the quality of multistability and use this measure to compare the double-resonance model with single-resonance models in χ(2) media. We also discuss the modulational instability of the double-resonance system and present physical estimates of the power required for soliton generation.