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• articleNo Access

#### Novel analytical solutions and optical soliton structures of fractional-order perturbed Kaup–Newell model and its application

The Kaup–Newell equation is used to model sub-picoseconds pulses that travel throughout optical fibers. The fractional-order perturbed Kaup–Newell model, which represents extensive waves parallel to the field of magnetic, is examined. In this paper, two analytical techniques named, improved F-expansion and generalized exp$(−ϕ(ζ))$-expansion techniques, are employed and new analytical solutions in generalized forms like bright solitons, dark solitons, multi-peak solitons, peakon solitons, periodic solitons and further wave results are assembled. These soliton solutions and other waves findings have important applications in applied sciences. The configurations of some solutions are shown in the form of graphs through assigning precise values to parameters, and their dynamics are described. The illustrated novel structures of some solutions also assist engineers and scientists in better grasping the physical phenomena of this fractional model. A comparison analysis has been given to explain the originality of the current findings compared to the previously achieved results. The results of computer simulations show that the procedures described are effective, simple, and efficient.

• articleNo Access

#### Singular manifold, auto-Bäcklund transformations and symbolic-computation steps with solitons for an extended three-coupled Korteweg-de Vries system

Korteweg-de Vries (KdV)-type models are frequently seen during the investigations on the optical fibers, cosmic plasmas, planetary oceans and atmospheres. In this paper, for an extended three-coupled KdV system, noncharacteristic movable singular manifold and symbolic computation help us bring about four sets of the auto-Bäcklund transformations with some solitons. All of our results rely on the coefficients in that system.

• articleNo Access

#### EXISTENCE AND STABILITY OF SOLITARY WAVES IN NON-LINEAR KLEIN–GORDON–MAXWELL EQUATIONS

We prove the existence and stability of non-topological solitons in a class of weakly coupled non-linear Klein–Gordon–Maxwell equations. These equations arise from coupling non-linear Klein–Gordon equations to Maxwell's equations for electromagnetism.

• articleNo Access

#### LONG-TIME ASYMPTOTICS OF THE TODA LATTICE FOR DECAYING INITIAL DATA REVISITED

The purpose of this article is to give a streamlined and self-contained treatment of the long-time asymptotics of the Toda lattice for decaying initial data in the soliton and in the similarity region via the method of nonlinear steepest descent.

• articleNo Access

#### STATIC PROPERTIES AND WAVEGUIDE MODES OF A WIDE LATERAL WINDOW JOSEPHSON JUNCTION

We developed an efficient hybrid mode expansion method to study the maximum tunneling current as a function of the external magnetic field for a 2D large area lateral window junction. We consider the inhomogeneity in the critical current density, which is taken a piecewise constant. The natural modes of the expansion in y, are the linearized eigen-modes around a static solution which satisfies the 1D sine-Gordon equation with the critical current variation in y, and the boundary conditions determined by the overlap component of the bias current, which can be inline or overlap like. The magnetic field along with the inline component of the bias current enters as a boundary condition on the modal amplitudes. We obtain fast convergent results and for a ratio of idle to window widths of w0/w = 4 (in units of λJ), only two modes are needed. A simple scaling is obtained for the maximum tunneling current as we vary the idle region width. We also present the linear electromagnetic waveguide modes taking into account the variation normal to the waveguide of the critical current and the capacitance.

• articleNo Access

#### ENERGY DYNAMICS IN A ONE-DIMENSIONAL APERIODIC ANHARMONIC LATTICE

We study the nature of collective excitations in classical anharmonic lattices with aperiodic and pseudo-random harmonic spring constants. The aperiodicity was introduced in the harmonic potential by using a sinusoidal function whose phase varies as a power-law, ϕ ∝ nν, where n labels the positions along the chain. In the absence of anharmonicity, we numerically demonstrate the existence of extended states and energy propagation for a sufficiently large degree of aperiodicity. Calculations were done by using the transfer matrix formalism (TMF), exact diagonalization and numerical solution of the Hamilton's equations. When nonlinearity is switched on, we numerically obtain a rich framework involving stable and unstable solitons.

• articleNo Access

#### FAST INTEGRATION OF ONE-DIMENSIONAL BOUNDARY VALUE PROBLEMS

Two-point nonlinear boundary value problems (BVPs) in both unbounded and bounded domains are solved in this paper using fast numerical antiderivatives and derivatives of functions of L2(-∞, ∞). This differintegral scheme uses a new algorithm to compute the Fourier transform. As examples we solve a fourth-order two-point boundary value problem (BVP) and compute the shape of the soliton solutions of a one-dimensional generalized Korteweg–de Vries (KdV) equation.

• articleNo Access

#### Optical computing with soliton trains in Bose–Einstein condensates

Optical computing devices can be implemented based on controlled generation of soliton trains in single and multicomponent Bose–Einstein condensates (BEC). Our concepts utilize the phenomenon that the frequency of soliton trains in BEC can be governed by changing interactions within the atom cloud [F. Pinsker, N. G. Berloff and V. M. Pérez-García, Phys. Rev. A87, 053624 (2013), arXiv:1305.4097]. We use this property to store numbers in terms of those frequencies for a short time until observation. The properties of soliton trains can be changed in an intended way by other components of BEC occupying comparable states or via phase engineering. We elucidate, in which sense, such an additional degree of freedom can be regarded as a tool for controlled manipulation of data. Finally, the outcome of any manipulation made is read out by observing the signature within the density profile.

• articleNo Access

#### A computational study of solitary wave solutions of Kawahara-type equations by meshless spectral interpolation method

In this paper, a meshless spectral radial point interpolation (MSRPI) method using weighted $θ$-scheme is formulated for the numerical solutions of a class of nonlinear Kawahara-type evolutionary equations. The formulated method is applied for simulation of single and double solitary waves motion, wave generation and oscillatory shock waves propagation. Quality of approximation is measured via discrete $L∞$, $L2$ and $Lrms$ error norms. Three invariant quantities corresponding to mass, momentum and energy are also computed for the method validation. Stability analysis of the proposed method is briefly discussed and verified computationally. Comparison of the obtained results are made with other existing results in the literature revealing the method superiority.

• articleNo Access

#### SOLITON ANTISOLITON SCATTERING IN (2+1) DIMENSIONS

We consider the scattering of solitons and antisolitons in a class of models in (2+1) dimensions. We point out that although in general the interaction forces between solitons and antisolitons are attractive, in some σ models they depend on the relative orientation between the solitons and antisolitons in their internal space. We discuss the scattering properties of such solitons and antisolitons.

• articleNo Access

#### TOPOLOGY DEPENDENCE IN LATTICE SIMULATIONS OF NON-LINEAR PDES ON A MIMD COMPUTER

We tested the parallelization of explicit schemes for the solution of non-linear classical field theories of complex scalar fields which are capable of simulating hadronic collisions. Our attention focused on collisions in a fractional model with a particularly rich inelastic spectrum of final states. Relativistic collisions of all types were performed by computer on large lattices (64 to 256 sites per dimension). The stability and accuracy of the objects were tested by the use of two other methods of solutions: Pseudo-spectral and semi-implicit. Parallelization of the Fortran code on a 64-transputer MIMD Volvox machine revealed, for certain topologies, communication deadlock and less-than-optimum routing strategies when the number of transputers used was less than the maximum. The observed speedup, for N transputers in an appropriate topology, is shown to scale approximately as N, but the overall gain in execution speed, for physically interesting problems, is a modest 2–3 when compared to state-of-the-art workstations.

• articleNo Access

#### A SEMI-LINEAR ELLIPTIC PDE MODEL FOR THE STATIC SOLUTION OF JOSEPHSON JUNCTIONS

In this study we derive a semi-linear Elliptic Partial Differential Equation (PDE) problem that models the static (zero voltage) behavior of a Josephson window junction. Iterative methods for solving this problem are proposed and their computer implementation is discussed. The preliminary computational results that are given, show the modeling power of our approach and exhibit its computational efficiency.

• articleNo Access

#### EFFECT OF GEOMETRY ON FLUXON WIDTH IN A JOSEPHSON JUNCTION

We investigate the electromagnetic influence of the surrounding idle (no tunneling) region on static fluxons in window Josephson junctions. We calculated the fluxon width as a function of the size of the idle region for three different window (active tunneling area) geometries, namely elongated truncated rhombus, rectangular and bow-tie and derived approximate expressions for the case of small and large idle regions. The window geometry affects both the fluxon width and the fluxon stability. One can define an effective λJ which depends on the junction width, the idle region width and the inductance ratio and has important consequences on the static and dynamic properties of window Josephson junctions. We also show the effect of the idle region on the maximum tunneling current as a function of the external magnetic field.

• articleNo Access

#### Split Mode Method for the Elliptic 2D Sine-Gordon Equation: Application to Josephson Junction in Overlap Geometry

We introduce a new type of splitting method for semilinear partial differential equations. The method is analyzed in detail for the case of the two-dimensional static sine-Gordon equation describing a large area Josephson junction with overlap current feed and external magnetic field. The solution is separated into an explicit term that satisfies the one-dimensional sine-Gordon equation in the y-direction with boundary conditions determined by the bias current and a residual which is expanded using modes in the y-direction, the coefficients of which satisfy ordinary differential equations in x with boundary conditions given by the magnetic field. We show by direct comparison with a two-dimensional solution that this method converges and that it is an efficient way of solving the problem. The convergence of the y expansion for the residual is compared for Fourier cosine modes and the normal modes associated to the static one-dimensional sine-Gordon equation and we find a faster convergence for the latter. Even for such large widths as w=10 two such modes are enough to give accurate results.

• articleNo Access

#### A NEW APPROACH TO THE ANALYSIS OF A NONCOMMUTATIVE CHERN–SIMONS THEORY

A novel approach to the analysis of a noncommutative Chern–Simons gauge theory with matter coupled in the adjoint representation has been discussed. The analysis is based on a recently proposed closed form Seiberg–Witten map which is exact in the noncommutative parameter.

• articleNo Access

#### BRIGHT SOLITONS MANAGED BY FESHBACH RESONANCE IN BOSE–EINSTEIN CONDENSATES

We review the recent experimental and theoretical advances in the generation of matter wave solitons in Bose–Einstein condensates. In particular, the controlled generation and dynamics of stable bright solitons by mean of Feshbach resonance techniques is discussed in details. Several aspects are taking into account, including the variation of the scattering length due to Feshbach resonance, the safe parameters against the collapse and the experimental implications of our scenario.

• articleNo Access

#### ON THE QUESTION OF REGULAR SOLITONS IN A NONCOMMUTATIVE MAXWELL–CHERN–SIMONS–HIGGS MODEL

The Maxwell–Chern–Simons model with scalar matter in the adjoint representation is analyzed from an alternative approach which is regular in the θ→0 limit. This method is complementary to the usual operator formalism applied to explore the nonperturbative solutions which give singular results in the θ→0 limit. The absence of any regular non-trivial lumpy solutions satisfying B–P–S bound has been conclusively demonstrated.

• articleOpen Access

#### Propagating q-field and q-ball solution

One possible solution of the cosmological constant problem involves a so-called q-field, which self-adjusts so as to give a vanishing gravitating vacuum energy density (cosmological constant) in equilibrium. We show that this q-field can manifest itself in other ways. Specifically, we establish a propagating mode (q-wave) in the nontrivial vacuum and find a particular soliton-type solution in flat spacetime, which we call a q-ball by analogy with the well-known Q-ball solution. Both q-waves and q-balls are expected to play a role for the equilibration of the q-field in the very early universe.

• articleNo Access

#### Index theorem for non-supersymmetric fermions coupled to a non-Abelian string and electric charge quantization

Non-Abelian strings are considered in non-supersymmetric theories with fermions in various appropriate representations of the gauge group U$(N)$. We derive the electric charge quantization conditions and the index theorems counting fermion zero modes in the string background both for the left-handed and right-handed fermions. In both cases we observe a non-trivial $N$ dependence.

• articleNo Access

#### Multi-component noncommutative coupled dispersionless system and its quasideterminant solutions

The multi-component noncommutative coupled dispersionless (NC-CD) system is presented. It has been shown that multi-component NC-CD system is integrable in the sense of exhibiting its Lax pair, zero-curvature representation, Darboux transformation and multisoliton solutions. Explicit expressions of multisoliton solutions of this noncommutative system have been computed and results have been compared with their commutative counterparts.