Narrow Results

Under investigation in this paper is a generalized Heisenberg ferromagnet (HF) equation which is named the Zhanbota-IIA equation. It is one of the integrable generalizations of the HF equation that plays an important role in nonlinear magnetization dynamics. Through the establishment of the N-fold Darboux transformation, a series of solutions will be obtained, including multi-solitons, one- and two-breathers, first- and higher-order rogue waves. Dynamic behaviors of those solutions will be analyzed, including several structures of rogue waves such as fundamental structure, triangular structure, ring structure and ring-fundamental structure, the coexistence of rogue waves and breathers, i.e. semi-rational solution and the interaction of two breathers.

The aim of this paper is to elucidate the existence of patterns for Keller–Segel-type models that are solutions of the traveling pulse form. The idea is to search for transport mechanisms that describe this type of waves with compact support, which we find in the so-called nonlinear diffusion through saturated flux mechanisms for the movement cell. At the same time, we analyze various transport operators for the chemoattractant. The techniques used combine the analysis of the phase diagram in dynamic systems together with its counterpart in the system of partial differential equations through the concept of entropic solution and the admissible jump conditions of the Rankine–Hugoniot type. We found traveling pulse waves of two types that correspond to those found experimentally.

This paper focuses on the numerical investigation of the fractal modification of the (3+1)-dimensional potential-Yu–Toda–Sasa–Fukuyama (YTSF) equation. A variational approach based on the two-scale fractal complex transformation and the variational principle is presented for solving this fractal equation. The fractal potential-YTSF equation can be transformed as the original potential-YTSF equation by means of the fractal complex transformation. Some fractal soliton-type solutions and fractal periodic wave solutions are provided by using the variational principle proposed by He, which are not touched in the existing literature. Some remarks about the variational formulation and the wave solutions for the original potential-YTSF equation by Manafian et al. [East Asian J. Appl. Math. 10(3) (2020) 549–565] are also given. Numerical results of the fractal wave solutions with different fractal dimensions and amplitudes are presented to show the propagation behavior.

A previously unknown bright N-soliton solution for an intermediate nonlinear Schrödinger equation of focusing type is presented. This equation is constructed as a reduction of an integrable system related to a Sato equation of a 2-component KP hierarchy for certain differential-difference dispersion relations. Bright soliton solutions are obtained in the form of double Wronskian determinants.

By using gauge transformations, we manage to obtain new solutions of (2 + 1)-dimensional Kadomtsev–Petviashvili (KP), Kaup–Kuperschmidt (KK) and Sawada–Kotera (SK) equations from nonzero seeds. For each of the preceding equations, a Galilean type transformation between these solutions u₂ and the previously known solutions u′₂ generated from zero seed is given. We present several explicit formulas of the single-soliton solutions for u₂ and u′₂, and further point out the two main differences of them under the same value of parameters, i.e., height and location of peak line, which are demonstrated visibly in three figures.

In the present paper we propose a new proof of the Grosset–Veselov formula connecting one-soliton solution of the Korteweg–de Vries equation to the Bernoulli numbers. The approach involves Eulerian numbers and Riccati's differential equation.

There exists a particular class of boundary value problems for integrable nonlinear evolution equations formulated on the half-line, called linearizable. For this class of boundary value problems, the Fokas method yields a formalism for the solution of the associated initial-boundary value problem, which is as efficient as the analogous formalism for the Cauchy problem. Here, we employ this formalism for the analysis of several concrete initial-boundary value problems for the nonlinear Schrödinger equation. This includes problems involving initial conditions of a hump type coupled with boundary conditions of Robin type.

We consider an optical pulse propagation in a one-dimensional nonlinear periodic structure doped uniformly with inhomogeneously broadening two-level atoms wherein the pulse propagation is governed by the nonlinear coupled mode-Maxwell Bloch equations. We investigate the pulse-train like periodic waves as well as bright and dark solitons near the photonic bandgap structure under the influence of self-induced transparency (SIT) effect. Further, we demonstrate that the resulting bright and dark SIT Bragg solitons may be realized both in anomalous and normal dispersion regimes, and this novel concept is ultimately the crux of this paper.

The internal motions of biomatter immersed in biofluid are investigated. The interactions between the fragments of biomatter and its surrounding biofluid are modeled using field theory. In the model, the biomatter is coupled to the gauge field representing the biofluid. It is shown that at non-relativistic limit various equation of motions, from the well-known Sine-Gordon equation to the simultaneous nonlinear equations, can be reproduced within a single framework.

In the present paper, we have investigated the solitonic characteristics of a pulse passing through an interface separating two nonlinear media. The first media is a thin film of gallium nanoparticles which show switching properties under optical excitation and second is a monomode optical fiber. Soliton propagation in three different phases of gallium nanoparticles have been analyzed by using the method of phase-plane analysis. Also, the critical power required for soliton propagation has been calculated.

Depending on their strength, the electron–phonon interactions in systems involving electron moving in deformable lattice of atoms can become very important for the dynamics of such systems and may lead to some very interesting phenomena eg. quasiparicle self trapping. We consider Metallic Carbon Nanotube with an excess electron. We choose 2- dimensional hexagonal lattice to be periodic and to have a large extension in one direction and a small extension in the other direction. We study the Modified Nonlinear Schrodinger Equation in Carbon Nanotube (10,10) where the modified term arises due to interaction between excess electron field and lattice distortion and gives stabilization to the solution. This interaction symbolizes strength of nonlinearity in the system. We solved this equation numerically using cylindrical coordinates and found that solutions depend crucially on electron- phonon interaction coefficient.

Solitons are nonlinear waves that remain invariant as they propagate. Precise control of dispersion and nonlinear effects govern soliton propagation. In recent years Photonic crystals (PhCs) have attracted a great deal of attention due to the facility to engineer and enhance both their nonlinear and dispersive effects. In this article we show soliton pulse analysis in GaInP Photonic Crystal Waveguides using AUTO bifurcation analysis tool. We have demonstrated pulse compression at moderately slow velocities in GaInP Photonic Crystal Waveguides. This is enabled by the enhanced self phase modulation and strong negative group velocity dispersion in the Photonic Crystal Waveguides.

We study axion strings with the electroweak gauge flux in the DFSZ axion model and show that these strings, called electroweak axions, exhibit superconductivity without fermionic zero modes. We also show that the primordial magnetic field in the early universe can induce a large electric current along the string. A pair of the strings carrying such a large current feels a net attractive force between them and can form a Y-shaped junction in the early universe, whose formation probability is roughly estimated to be 1/2.

New soliton solutions for thick branes in 4 + 1 dimensions are considered in this article. In particular, brane models based on the sine-Gordon (SG), φ⁴ and φ⁶ scalar fields are investigated; in some cases Z₂ symmetry is broken. Besides, these soliton solutions are responsible for supporting and stabilizing the thick branes. In these models, the origin of the symmetry breaking resides in the fact that the modified scalar field potential may have non-degenerate vacuua and these non-degenerate vacuua determine the cosmological constant on both sides of the brane. At last, in order to explore the particle motion in the neighborhood of the brane, the geodesic equations along the fifth dimension are studied.

It is known that ultra-extreme Kerr-Newman (KN) solution (a >> m) produces the gravitational and EM fields of the electron and has a topological defect which may be regularized by a solitonic source, formed as a false-vacuum bubble filled by Higgs condensate in a supersymmetric superconducting state. Structure and stability of this source is determined by Bogomolnyi equations as a BPS-saturated soliton of the oscillon type. The Principal Null Congruences of the KN solution determine consistent embedding of the Dirac equation, which acquires the mass from the Higgs condensate inside the soliton, indicating that this soliton forms a bag model. Shape of this bag is unambiguously determined by BPS-bound. The bag turns out to be flexible and takes the form of a very thin disk, which is completed by a ring-string along its sharp boundary. The ring-string traveling waves generate extra deformations of the bag creating a circulating singular pole. Bag model of the KN source integrates the dressed and pointlike electron in a bag-string-quark system, which removes the conflict between the point-like electron of the Dirac theory and the required gravitational soliton model.