Single Kink Research Articles

Nonperturbative phase boundaries in the Gross-Neveu model from a stability analysis

Two out of three phase boundaries of the 1+1-dimensional Gross-Neveu model in the chiral limit can be obtained from a standard, perturbative stability analysis of the homogeneous phases. The third one separating the massive homogeneous phase from the kink crystal is nonperturbative and could so far only be inferred from the full solution of the model. We show that this phase boundary can also be obtained via a modified stability analysis, based on the thermodynamic potential of a single kink or baryon. The same method works for the massive Gross-Neveu model, so that all phase boundaries of the Gross-Neveu model could have been predicted quantitatively without prior knowledge of the full crystal solution. Published by the American Physical Society 2024

Soliton-based modeling of nano-ionic currents in transmission line

Many nonlinear evolution equations, such as the nano-ionic currents (NIC) equation, are used extensively in many scientific and technological domains particularly in nanoelectronics and bioelectronics. The mathematical modeling of NIC phenomena is vital for understanding their behavior and optimizing device performance. Our research leverages an array of mathematical methods, including multi-wave analysis, periodic wave solutions, lump soliton dynamics, breather wave phenomena, homoclinic breathers, M-shaped waveforms, and rogue wave analysis. Additionally, our investigation encompasses the exploration of single kink and double kink configurations, interactions between periodic and kink waves, interaction between M shaped with kink and rogue, interaction between M shaped with one kink, interaction between M shaped with kink and periodic, interaction between M shaped with two kinks as well as periodic wave interactions with lump waves. To further emphasize the structure of solutions derived from particular parameter choices, we include three-dimensional, two-dimensional, streamplot, and contour graphs.

Krauklis wave propagation within a complex fracture system: Modeling via a two-dimensional time-harmonic boundary element method.

Fluid-filled fractures involving kinks and branches result in complex interactions between Krauklis waves-highly dispersive and attenuating pressure waves within the fracture-and the body waves in the surrounding medium. For studying these interactions, we introduce an efficient 2D time-harmonic elastodynamic boundary element method. Instead of modeling the domain within a fracture as a finite-thickness fluid layer, this method employs zero-thickness, poroelastic Linear-Slip Interfaces to model the low-frequency, local fluid-solid interaction. Using this method, the scattering of Krauklis waves by a single kink along a straight fracture and the radiation of body waves generated by Krauklis waves within complex fracture systems are examined.

Exact solutions of the (2+1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(2+1)$$\\end{document}-dimensional Zoomeron model arising in nonlinear optics via mapping method

The Zoomeron model covers particular kinds of solitons with distinctive properties that appear in several physical scenarios, such as, fluid dynamics, nonlinear optics and laser physics. First time utilising the mapping method, we determine the analytical solution to the described model, including several novel dynamical behaviours. Through symbolic computation, we are able to derive the breather waves, kink waves, dark soliton, singular soliton, periodic soliton and bright soliton of this model. Additionally, we encounter single kink waves and single breather waves. We find novel hyperbolic trigonometric, rational and elliptic functions. Modelling our observations with MATLAB tools and producing many 3D graphs. The results obtained will be crucial for further research on complicated nonlinear models.

On Multiple-Type Wave Solutions for the Nonlinear Coupled Time-Fractional Schrödinger Model

Recently, nonlinear fractional models have become increasingly important for describing phenomena occurring in science and engineering fields, especially those including symmetric kernels. In the current article, we examine two reliable methods for solving fractional coupled nonlinear Schrödinger models. These methods are known as the Sardar-subequation technique (SSET) and the improved generalized tanh-function technique (IGTHFT). Numerous novel soliton solutions are computed using different formats, such as periodic, bell-shaped, dark, and combination single bright along with kink, periodic, and single soliton solutions. Additionally, single solitary wave, multi-wave, and periodic kink combined solutions are evaluated. The behavioral traits of the retrieved solutions are illustrated by certain distinctive two-dimensional, three-dimensional, and contour graphs. The results are encouraging, since they show that the suggested methods are trustworthy, consistent, and efficient in finding accurate solutions to the various challenging nonlinear problems that have recently surfaced in applied sciences, engineering, and nonlinear optics.

Phase-field dislocation dynamics simulations of temperature-dependent glide mechanisms in niobium

In this work, we present a three-dimensional ab-initio informed phase-field-dislocation dynamics model combined with Langevin dynamics to investigate glide mechanisms of edge and screw dislocations at finite temperatures in Nb. Over a temperature range of 150 K to 600 K, calculations reveal that the screw dislocation changes its mode of glide at two distinct temperatures. At 200–220 K, the glide mechanism changes from single kink pair motion to multiple kink pair motion. The kink pair enthalpies quantitatively agree with those extracted from experimental tests on Nb single crystals. Between 300 K and 350 K the glide mode transitions to overlapping kink pairs and glide is smooth (non-jerky). The screw to edge mobility ratio is seen to peak at 350 K and plateau thereafter. These two temperatures coincide with temperatures at which yield strengths in Nb are observed to become thermally insensitive and athermal, respectively.

Mechanism of thermally-activated prismatic slip in Mg

Prismatic slip of the screw <a> dislocation in magnesium at temperatures ≳ 150 K is understood to be governed by double-cross-slip of the stable basal screw through the unstable prism screw and back to the basal screw, with the activation energy controlled by the formation energy of two basal-basal kinks. However, atomistic studies of the double-kink process predict activation energies roughly twice those derived experimentally. Here, a new mechanism of prism glide is proposed, analyzed theoretically, and demonstrated qualitatively and quantitatively via direct molecular dynamics (MD) simulations. The new mechanism is intrinsically 3d, and involves the nucleation of a single kink at the junction where a 3d prismatic dislocation loop transitions from the basal screw segment to non-screw prismatic character. The relevant kink energies are calculated using recently-developed Neural-Network Potentials (NNPs) for Mg that show good agreement versus DFT for basal and prism <a> dislocations, enabling a parameter-free analytic model for the activation barrier. Direct MD simulations show both operation of the precise proposed mechanism and a stress-dependent activation barrier that agrees reasonably with the analytic model. Predictions of dislocation velocity compare very well with in-situ TEM data, and macroscopic strength versus temperature can also be understood. Overall, the new intrinsically 3d mechanism for dislocation glide due to single kink nucleation rather than double-kink nucleation explains key features of the prismatic slip in Mg and may have broader applicability in other metals where kink nucleation processes control thermally-activated flow.

Collision phenomena among the solitons, periodic and Jacobi elliptic functions to a (3+1)-dimensional Sharma-Tasso-Olver-like model

In this manuscript, we consider a (3+1)-dimensional Sharma-Tasso-Olver-like (STOL) model, which can be used to describe dispersive wave phenomena in optics, plasmas, quantum physics, and others. Based on the simplified Hirota approach, the n-soliton solutions are obtained. We observe that the collisions are non-elastic fusion or fission phenomena where some kink waves disappear due to soliton fusion, or a single kink wave splits into more kink waves due to soliton fusion. We derive kinky-lump breather, combo line kink and kinky-lump breather, and a pair of kinky-lump breather wave solutions that degenerate from two-, three- and four-solitons respectively by choosing complex conjugate values involving free parameters. Moreover, we demonstrate a few new collisions of the Jacobi elliptic sine function with one soliton, and a periodic cosine function which provides kinky-periodic waves and double-periodic waves. All special properties of those collision solutions are illustrated with the 3D, density and contour plots.

Kink–antikink stripe interactions in the two-dimensional sine–Gordon equation

The main focus of the present work is to study quasi-one-dimensional kink–antikink stripes embedded in the two-dimensional sine–Gordon equation. Using variational techniques, we reduce the interaction dynamics between a kink and an antikink stripe on their respective time and space dependent widths and locations. The resulting reduced system of coupled equations is found to accurately describe the width and undulation dynamics of a single kink stripe as well as that of two interacting ones. As an aside, we also discuss two related topics: the computational identification of the kink center and its numerical implications and alternative perturbative and multiple scales approaches to the transverse direction induced dynamics for a single kink stripe in the two-dimensional realm.

Twisted kink crystal in holographic superconductor

Holographic superconductor model represents various inhomogeneous solutions with homogeneous sources. In this paper, we study inhomogeneous structures in the presence of the homogeneous current and the chemical potential. We find single complex kink condensates, multiple complex kinks condensates and twisted kink crystal condensates in which both the amplitude and the phase of the order parameter modulate in space. Analyzing the gauge-invariant phase difference in the single complex kink condensates, we find the non-monotonic behaviour with respect to the current. We confirm that the multiple complex kinks condensates and the twisted kink crystal condensates are well described by the analytic solutions obtained from the Gross-Neveu model or the Nambu-Jona-Lasinio model. We also analyze the thermodynamic stability of the complex kink(s) condensates by computing the free energy. Our results imply that holographic superconductor model provides the boundary physics which is effectively represented by the Ginzburg-Landau theory with higher corrections.

Kink dynamics in a nonlinear beam model

In this paper, we study the single kink and the kink-antikink collisions of a nonlinear beam equation bearing a fourth-derivative term. We numerically explore some of the key characteristics of the single kink both in its standing wave and in its traveling wave form. A point of emphasis is the study of kink-antikink collisions, exploring the critical velocity for single-bounce (and separation) and infinite-bounce (where the kink and antikink trap each other) windows. The relevant phenomenology turns out to be dramatically different than that of the corresponding nonlinear Klein-Gordon (i.e., ϕ4) model. Our computations show that for small initial velocities, the kink and antikink reflect nearly elastically without colliding. For an intermediate interval of velocities, the two waves trap each other, while for large speeds a single inelastic collision between them takes place. Lastly, we briefly touch upon the use of collective coordinates (CC) method and their predictions of the relevant phenomenology. When one degree of freedom is used in the CC approach, the results match well the numerical ones for small values of initial velocity. However, for bigger values of initial velocity, it is inferred that more degrees of freedom need to be self-consistently included in order to capture the collision phenomenology.

Statistical mechanics of kinks on a gliding screw dislocation

The ability of a body-centered cubic metal to deform plastically is limited by the thermally activated glide motion of screw dislocations, which are line defects with a mobility exhibiting complex dependence on temperature, stress, and dislocation segment length. We derive an analytical expression for the velocity of dislocation glide, based on a statistical mechanics argument, and identify an apparent phase transition marked by a critical temperature above which the activation energy for glide effectively halves, changing from the formation energy of a double kink to that of a single kink. The analysis is in quantitative agreement with direct kinetic Monte Carlo simulations.

Iterated \u03d54 kinks

A first order equation for a static ϕ4 kink in the presence of an impurity is extended into an iterative scheme. At the first iteration, the solution is the standard kink, but at the second iteration the kink impurity generates a kink-antikink solution or a bump solution, depending on a constant of integration. The third iterate can be a kink-antikink-kink solution or a single kink modified by a variant of the kink’s shape mode. All equations are first order ODEs, so the nth iterate has n moduli, and it is proposed that the moduli space could be used to model the dynamics of n kinks and antikinks. Curiously, fixed points of the iteration are ϕ6 kinks.

Kink-type solutions of the SIdV equation and their properties.

We study the nonlinear integrable equation, ut + 2((uxuxx)/u) = ϵuxxx, which is invariant under scaling of dependent variable and was called the SIdV equation (see Sen et al. 2012 Commun. Nonlinear Sci. Numer. Simul. 17, 4115–4124 (doi:10.1016/j.cnsns.2012.03.001)). The order-n kink solution u[n] of the SIdV equation, which is associated with the n-soliton solution of the Korteweg–de Vries equation, is constructed by using the n-fold Darboux transformation (DT) from zero ‘seed’ solution. The kink-type solutions generated by the onefold, twofold and threefold DT are obtained analytically. The key features of these kink-type solutions are studied, namely their trajectories, phase shifts after collision and decomposition into separate single kink solitons.

Atomistic simulations of carbon effect on kink-pair energetics of bcc iron screw dislocations

The mechanical properties of body-centered cubic metals at low temperatures are strongly influenced by the solute atoms, which could be relatively complex as either hardening or softening effects would be introduced depending on the solute concentration and temperature. One major impact is that solute atoms can affect both kink formation and motion during screw dislocation gliding, which plays an important role in plastic behavior of bcc metals. In this study, atomistic simulations are conducted on the carbon-affected kinking of a screw dislocation in iron using the nudged elastic band method. When kink nucleates alongside a carbon atom, the kink formation energy decreases as the carbon transits to a stronger binding site, and vice versa. When a single kink meets the carbon during propagation, the sideward motion of the kink is impeded. With regard to the different temperatures and solute concentrations, the softening and hardening effects induced by carbon solutes in iron can be explained by the complex atomistic process.

Roles of kink on the thermal transport in single polyethylene chains

The trans-gauche state transformation commonly exists in polymers. However, the fundamental understanding of the roles of kink (gauche state) on the thermal energy transport in polymer chains is rather limited. From atomic simulations, we show that kinks greatly scatter phonons in single polyethylene chains, and even a single kink can reflect more than half of the phonons. Further studies show that kinks not only add extra thermal resistance to the chain but also break the whole chain into small segments and each with reduced thermal conductivity. A simple series thermal resistance model is proposed to estimate the effective thermal conductivity of single polymer chains with multiple kinks.

Dynamics of mixed lump-solitary waves of an extended (2 + 1)-dimensional shallow water wave model

To explore the features of lump solutions, which are local in every direction of space, a (2+1)-dimensional extended shallow water wave model is studied, based on its bilinear representation. Several ansatzes have been utilized to determine single lump waves, lump-kink waves, single kinks and multi-lumps leading to breathers in terms of function patterns for the model. Through analyzing interactions between solitons, the impact of free parameters involved in the solutions on interaction types is exhibited. We determine a condition on the parameters under which a single kink wave can be converted into a multi-lump wave. To illustrate the interaction of exponential and periodic function waves, we show that multi-lump waves in the form of breather waves especially come into sight as a straight line or an X shape. To realize dynamics, we make various graphical analyses on the presented solutions, which gives an essential improvement in the physical realizing of higher-dimensional lump waves in oceanography and nonlinear optics.

${\boldsymbol~K}$-fields domain wall

In this paper, we construct the single kink and double kink domain wall solutions by considering the non-canonical $K$-field in a flat five-dimensional spcaetime. The localization of chiral fermion is also investigated with the Yukawa coupling mechanism, and the corresponding massless left-chiral fermion can be localized on the $K$-field two types domain walls. The effective potentials of the chiral fermion on the two types domain walls will have different behaviors and the corresponding effective potential of the chiral fermion on the double-kink domain wall will have double well, and which means that the double kink domain wall will have mroe richer internal structures.

Kinks and antikinks of buckled graphene: A testing ground for the φ4 field model

Kinks and antikinks of the classical phi^4 field model are topological solutions connecting its two distinct ground states. Here we establish an analogy between the excitations of a long graphene nanoribbon buckled in the transverse direction and phi^4 model results. Using molecular dynamics simulations, we investigated the dynamics of a buckled graphene nanoribbon with a single kink and with a kink-antikink pair. Several features of phi^4 model have been observed including the kink-antikink capture at low energies, kink-antikink reflection at high energies, and a bounce resonance. Our results pave the way towards the experimental observation of a rich variety of phi^4 model predictions based on graphene.

Nonlinear defect localized modes and composite gray and anti-gray solitons in one-dimensional waveguide arrays with dual-flip defects

We study families of stationary nonlinear localized modes and composite gray and anti-gray solitons in a one-dimensional linear waveguide array with dual phase-flip nonlinear point defects. Unstaggered fundamental and dipole bright modes are studied when the defect nonlinearity is self-focusing. For the fundamental modes, symmetric and asymmetric nonlinear modes are found. Their stable areas are studied using different defect coefficients and their total power. For the nonlinear dipole modes, the stability conditions of this type of mode are also identified by different defect coefficients and the total power. When the defect nonlinearity is replaced by the self-defocusing one, staggered fundamental and dipole bright modes are created. Finally, if we replace the linear waveguide with a full nonlinear waveguide, a new type of gray and anti-gray solitons, which are constructed by a kink and anti-kink pair, can be supported by such dual phase-flip defects. In contrast to the usual gray and anti-gray solitons formed by a single kink, their backgrounds on either side of the gray hole or bright hump have the same phase.