Antikink Soliton Research Articles

Intrinsical localization of both topological (anti-kink) envelope and gray (black) gap solitons of the condensed bosons in deep optical lattices.

By developing quasi-discrete multiple-scale method combined with tight-binding approximation, a novel quadratic Riccati differential equation is first derived for the soliton dynamics of the condensed bosons trapped in the optical lattices. For a lack of exact solutions, the trial solutions of the Riccati equation have been analytically explored for the condensed bosons with various scattering length as. When the lattice depth is rather shallow, the results of sub-fundamental gap solitons are in qualitative agreement with the experimental observation. For the deeper lattice potentials, we predict that in the case of as>0, some novel intrinsically localized modes of symmetrical envelope, topological (kink) envelope, and anti-kink envelope solitons can be observed within the bandgap in the system, of which the amplitude increases with the increasing lattice spacing and (or) depth. In the case of as<0, the bandgap brings out intrinsically localized gray or black soliton. This well provides experimental protocols to realize transformation between the gray and black solitons by reducing light intensity of the laser beams forming optical lattice.

The pulses propagation beyond ultra-short range in the systems of optical communication via higher-order nonlinear Schrödinger equation with derivative non-Kerr nonlinear terms

The higher-order nonlinear Schrodinger equation with derivative non-Kerr nonlinear terms is studied in this work. The pulses propagation beyond ultra-short range in the systems of optical communication is described through this dynamical model. The modified extended direct algebraic technique is utilized for deriving different kinds exact solutions such as bright–dark solitons, kink and anti-kink solitons, solitary waves, periodic solutions and elliptic function solutions of this dynamical model. These achieved exact solutions are more general and are useful to researcher for understanding physical phenomena. The structures of some solutions at suitable values of parameters are presented and helpful for knowing the physical interpretation. Several solutions are novel by comparing these solutions with existing solutions. The power and effectiveness of current can observed form constructed solutions.

Construction of traveling and solitary wave solutions for wave propagation in nonlinear low-pass electrical transmission lines

In this study, our aim to constructed the traveling and solitary wave solutions for nonlinear evolution equation describe the wave propagation in nonlinear low-pass electrical transmission lines by implemented the modification of mathematical method. We obtained the new and more general solutions in rational, trigonometric, hyperbolic type which represent to kink and anti-kink wave solitons, bright-dark solitons and traveling waves. The physical interpretation of some results demonstrated by graphically with symbolic computation. We are hopefully determined results have numerous applications in optical fiber, geophysics, fluid dynamics, laser optics, engineering, and many other various kinds of applied sciences. The complete investigation prove that proposed technique is more reliable, efficient, straightforward, and powerful to investigate various kinds of nonlinear evolution equations involves in geophysics, fluid dynamics, nonlinear plasma, chemistry, biology, and field of engineering.

An energy-based discontinuous Galerkin method for semilinear wave equations

We generalize the energy-based discontinuous Galerkin method proposed in [1] to second-order semilinear wave equations. A stability and convergence analysis is presented along with numerical experiments demonstrating optimal convergence for certain choices of the interelement fluxes. Applications to the sine-Gordon equation include simulations of breathers, kink, and anti-kink solitons.

Spherical Symmetric Kink-Like Configurations of Spinor and Gravitational Fields

The present research work deals with an extension of a previous work [Exact Soliton-like spherical symmetric solutions of the Heisenberg-Ivanenko type nonlinear spinor field equation in gravitational theory, Journal of Applied Mathematics and Physics, 2020, 8, 1236-1254] to Spherical Symmetric Kink-Like Configurations of Spinor and Gravitational Fields. We have obtained exact kink-like static spherical symmetric solutions to the self-consistent system of spinor and gravitational fields equations. The Einstein’s field equation shave been solved by the Liouville method. The principal difference between kink soliton with antikink soliton has been established. The nonlinear terms in the lagrangian are arbitrary functions F(IS) depending on the invariant IS = S2= ( )2. It is shown that the initial set of the Einstein and spinor field equations have regular solutions with a localized energy density of the spinor field only if m = 0 (m is the mass parameter in the spinor field equations). Equations with polynomial nonlinearities are thoroughly scrutinized. Let us emphasize that the spinor field with polynomial nonlinearities has a regular solutions with localized, positive and alternating energy density and finite total energy. In addition, the total charge and the total spin are also finte. We have also obtained exact solutions to the linear spinor field equations. We remarked that in this case soliton-like solutions are absent. Furthermore, we note that the properties of regular localized solutions depend on the symmetry and the nonlinear terms in the lagrangian of the self-consistent system of gravitational and spinor fields.

New dark-bright soliton in the shallow water wave model

In this paper, we employ the sine-Gordon expansion method to shallow water wave models which are Kadomtsev-Petviashvili-Benjamin-Bona-Mahony and the Benney-Luke equations. We construct many new complex combined dark-bright soliton, anti-kink soliton solutions for the governing models. The 2D, 3D and contour plots are given under the suitable coefficients. The obtained results show that the approach proposed for these completely integrable equations can be used effectively.

Analytical methods via bright–dark solitons and solitary wave solutions of the higher-order nonlinear Schrödinger equation with fourth-order dispersion

In this research work, we investigated the higher-order nonlinear Schrödinger equation (NLSE) with fourth-order dispersion, self-steepening, nonlinearity, nonlinear dispersive terms and cubic-quintic terms which is described as the propagation of ultra-short pulses in fiber optics. We apply the modification form of extended auxiliary equation mapping method to find the new exact and solitary wave solutions of higher-order NLSE. As a result, new solutions are obtained in the form of solitons, kink–anti-kink type solitons, bright–dark solitons, traveling wave, trigonometric functions, elliptic functions and periodic solitary wave solutions. These new different types of solutions show the power and fruitfulness of this new method and also show two- and three-dimensional graphically with the help of computer software Mathematica. These new solutions have many applications in the field of physics and other branches of physical sciences. We can also solve other higher-order nonlinear partial differential equations (NPDEs) involved in mathematical physics and other various branches of physical sciences with this new technique.

Elliptic function soliton solutions of the higher-order nonlinear dispersive Kundu–Eckhaus dynamical equation with applications and stability

In this paper, we employ the four mathematical methods, namely improved simple equation method (SEM), modified extended SEM, generalized exp $$(-\Phi (\xi ))$$ -expansion technique and modified extended mapping technique, and attain exact solutions in various forms of Kundu–Eckhaus (K–E) equation. The wave solutions in the forms of bright and dark solitons, periodic solitary wave, kink and anti-kink soliton, trigonometric and hyperbolic trigonometric function and rational function are achieved. The movements of few results are presented graphically, which are useful to mathematician and physician for understanding the complex phenomena. The standard linear stability analysis is employed to examine the stability of the equation. This shows that exact solutions are stable. The results obtained are novel in nature and have good potential application values. The results demonstrate that these techniques are simple, effective and more powerful to solve nonlinear evolution equations.

Ion-acoustic solitary wave solutions of nonlinear damped Korteweg–de Vries and damped modified Korteweg–de Vries dynamical equations

By using the reductive perturbation technique, the nonlinear dust ion-acoustic solitary wave models of the damped Korteweg–de Vries (D-KdV) and modified damped Korteweg–de Vries (D-mKdV) equations are formulated. We constructed the more general and new solitary wave solutions of nonlinear damped KdV and damped mKdV equations by using the modified mathematical technique. These obtained solutions are more useful in the development of quantum plasma, dynamics of solitons, dynamics of adiabatic parameters, dynamics of fluid and problems of biomedical, industrial phenomena. The new solutions are obtained in the shape of dark solitons, bright solitons, traveling wave and kink and anti-kink wave solitons. We show the physical structure of new solutions by two and three-dimensions graphical to know the physical interpretation of different structure of dust ion-acoustic solitary wave. The calculations show that this new technique is more powerful, effective, straightforward, and fruitfulness to study analytically other nonlinear complex physical models in plasma physics, mathematical physics, fluid mechanics, hydrodynamics, mathematical biology and many other physical sciences.

Propagation of kink and anti-kink wave solitons for the nonlinear damped modified Korteweg–de Vries equation arising in ion-acoustic wave in an unmagnetized collisional dusty plasma

In this research work, we investigate the dust ion-acoustic solitary wave in an unmagnetized collisional dusty plasma, which consists on ions having positive charge, dust fluid with negative charge, q nonextensive electrons and background neutral particles. We formulated nonlinear model by the damped modified Korteweg–de Vries (D-mKdV) equation by applying reductive perturbation technique. We also constructed the new solitary wave solutions for nonlinear D-mKdV equation with the help of two techniques. The obtained solutions are new and general and having the structure in the form of solitons, kink and antikink wave solitons, traveling waves, periodic solitary wave and we also show the structure of obtained solutions by two-dim and three-dim graphical by using the Mathematica to know the physical interpretation of different structure of DIASWs. These obtained solutions are more useful in the development of quantum plasma, dynamics of solitons, dynamics of fluid, problems of biomedical, dynamics of adiabatic parameters, industrial phenomena and many other branches. The calculations show that these techniques are more effective, fruitfulness and powerful to investigate analytical other nonlinear physical models of PDEs involves in Mathematical physics, plasma physics, Geo physics, fluid mechanics, hydrodynamics, mathematical biology, field of engineering and many other physical sciences.

Construction of solitary wave solutions of some nonlinear dynamical system arising in nonlinear water wave models

The higher order of nonlinear partial differential equations in mathematical physics is studied. We used the analytical mathematical methods of the nonlinear (3+1)-dimensional extended Zakharov–Kuznetsov dynamical, modified KdV–Zakharov–Kuznetsov and generalized shallow water wave equations to demonstrate the efficiency and validity of the proposed powerful technique. The shallow water wave models have been applied in tidal waves and weather simulation. Exact wave solutions of these models in various forms such as Kink and anti-Kink solitons, bright–dark soliton, solitary wave and periodic solutions are constructed that have plenty of applications in diverse areas of physics. Graphically, we presented the movement of some obtained solitary wave solutions that aids in understanding the physical phenomena of these models.

Dispersive Solitary Wave Solutions of Strain Wave Dynamical Model and Its Stability

In the materials of micro-structured, the propagation of wave modeling should take into account the scale of various microstructures. The different kinds solitary wave solutions of strain wave dynamical model are derived via utilizing exp(−ϕ(ξ))-expansion and extended simple equation methods. This dynamical equation plays a key role in engineering and mathematical physics. Solutions obtained in this work include periodic solitary waves, Kink and anti-Kink solitary waves, bell-shaped solutions, solitons, and rational solutions. These exact solutions help researchers for knowing the physical phenomena of this wave equation. The stability of this dynamical model is examined via standard linear stability analysis, which authenticate that the model is stable and their solutions are exact. Graphs are depicted for knowing the movements of some solutions. The results show that the current methods, by the assist of symbolic calculation, give an effectual and direct mathematical tools for resolving the nonlinear problems in applied sciences.

Analytic study on chirped optical solitons in nonlinear metamaterials with higher order effects

The ultrashort pulse propagation in optical metamaterials (OMMs) modeled by a generalized nonlinear Schrödinger equation with higher order effects is studied, in the present paper. To this end, by considering a complex envelope and a specific nonlinear chirp ansatz, a wide range of exact chirped soliton solutions are derived in the presence of the pseudo-quintic nonlinearity and the self-steepening effect. Exact solutions include kink and anti-kink chirped soliton solutions that are retrieved through the use of newly well-designed methods. The complex envelopes presented herein provide new specific nonlinear shock wave structures in OMMs which are vital for numerical and experimental verifications.

Miscellaneous new traveling waves in metamaterials by means of the new extended direct algebraic method

In this paper, we investigate miscellaneous new traveling wave solutions of the generalized nonlinear Schrödinger equation modeling few-cycle pulse propagation in metamaterials by the new extended direct algebraic method. As a result, we construct various hyperbolic and trigonometric functions solutions and for some appropriated parameters we obtain exact solutions including kink, antikink, breathers, dark and bright solitons.

Optical soliton solutions for nonlinear Schrödinger equation

This piece of research is devoted to study nonlinear Schrödinger equation (NLSE) along with perturbation terms and its soliton solutions. The model is integrated via G′G2-expansion approach and the first integral method. Dark, singular and periodic soliton solutions are retrieved along with kink and anti-kink type soliton solutions that emerged from the two integration schemes applied to the model. Many forms of combo soliton solutions are also listed as a byproduct. The restrictions on the parameters for the existence of these solitons are also presented.

Analysis of a novel lattice hydrodynamic model considering predictive effect and flow integral

By taking the predictive effect and flow integral into consideration, we propose an improved lattice hydrodynamic model. Firstly, we apply linear stability analysis to acquire the linear stability condition, which can be used to explain the influence of predictive effect and flow integral on traffic flow stability. After that, the modified Korteweg–de Vries (mKdV) equation is derived through the nonlinear theory, which demonstrates that the solution of mKdV equation can describe traffic jams. Besides, the kink–antikink soliton wave is obtained through solving the mKdV equation, which can describe the propagation characteristics of the traffic density waves. Furthermore, we try to explore how predictive effect and flow integral influence the stability of traffic flow through numerical simulations. Finally, we find that the stability of traffic flow can be efficiently improved with the consideration of the two factors by observing and analyzing the numerical results.

Construction of new solitary wave solutions of generalized Zakharov-Kuznetsov-Benjamin-Bona-Mahony and simplified modified form of Camassa-Holm equations

AbstractIn this research work, for the first time we introduced and described the new method, which is modified extended auxiliary equation mapping method. We investigated the new exact traveling and families of solitary wave solutions of two well-known nonlinear evaluation equations, which are generalized Zakharov-Kuznetsov-Benjamin-Bona-Mahony and simplified modified forms of Camassa-Holm equations. We used a new technique and we successfully obtained the new families of solitary wave solutions. As a result, these new solutions are obtained in the form of elliptic functions, trigonometric functions, kink and antikink solitons, bright and dark solitons, periodic solitary wave and traveling wave solutions. These new solutions show the power and fruitfulness of this new method. We can solve other nonlinear partial differential equations with the use of this method.

Sine-Gordon Solitons and Breathers in Rod-like Magnetic Liquid Crystals under External Magnetic Field**Supported by the Basic Scientific Research Project of Provincial Colleges and Universities in Heilongjiang Province under Grant No. KJCXZD201723, the Youth Science Foundations of Heilongjiang University under Grant No. QL201606

To study the nonlinear phenomena in rod-like magnetic liquid crystals (RMLCs), this paper establishes the dynamic model of molecular motion when giving a twisting disturbance to the molecules under external magnetic field. We find the twist of the molecules under magnetic field can be propagated in the form of a traveling wave. The dynamic equation of the molecular twisting we derived satisfies the form of Sine-Gordon equation. We obtain two solutions of the Sine-Gordon equation by theoretical calculation: the kink and anti-kink solitons and breathers. The characteristics of those solitons and breathers are discussed.

Mathematical methods via construction of traveling and solitary wave solutions of three coupled system of nonlinear partial differential equations and their applications

Abstract In this research work, we applying the modification form of extended auxiliary equation mapping method on three couple system of nonlinear ovulation equations which have odd and even partial derivatives. We investigated the new exact traveling and solitary wave solutions of coupled Whitham-Broer-Kaup, (2 + 1)-dimensional Broer-Kaup-Kupershmit and Drinfel’d-Sokolow-Wilson equations. We applied successfully this new method and obtained the new form of exact traveling and solitary wave solutions. As a results, obtained new solutions in the form of solitons, bright and dark solitons, kink and anti-kink type solitons, traveling wave, periodic solitary wave,trigonometric functions and elliptic functions solutions. These new different type of solutions are show the effectiveness and power of this new method and also show two and three dimensional graphically with the help of computer software Mathematica. These new solutions have many applications in the field of physics and other branches of applied science. We can also be solved other couple system of partial differential equations by this new technique.

Dynamics of optical solitons with Radhakrishnan–Kundu–Lakshmanan model via two reliable integration schemes

This work is devoted to the extraction of optical solitons with Radhakrishnan–Kundu–Lakshmanan model in the presence of Kerr law media with the aid of two versatile integration tools, namely, the modified simple equation and exp(−φ(q)) method. A plethora of traveling wave solutions including dark, singular, periodic singular, kink and anti kink soliton solutions are retrieved along with their graphical depiction. The validity conditions for these solutions are also listed.