Abstract: The spectral properties of two special classes of Jacobi operators are studied. For the first class represented by the -dimensional real Jacobi matrices whose entries are symmetric with respect to the secondary diagonal, a new polynomial identity relating the eigenvalues of such matrices with their matrix entries is obtained. In the limit this identity induces some requirements, which should satisfy the scattering data of the resulting infinite-dimensional Jacobi operator in the half-line, of which super- and subdiagonal matrix elements are equal to . We obtain such requirements in the simplest case of the discrete Schrödinger operator acting in , which does not have bound and semibound states and whose potential has a compact support. PubDate: Tue, 16 Oct 2018 08:15:49 +000

Abstract: In this article, we investigate an integrable weakly coupled nonlocal nonlinear Schrödinger (WCNNLS) equation including its Lax pair. Afterwards, Darboux transformation (DT) of the weakly coupled nonlocal NLS equation is constructed, and then the degenerated Darboux transformation can be got from Darboux transformation. Applying the degenerated Darboux transformation, the new solutions (,) and self-potential function are created from the known solutions (,). The (,) satisfy the parity-time (PT) symmetry condition, and they are rational solutions with two free phase parameters of the weakly coupled nonlocal nonlinear Schrödinger equation. From the plots of solutions, the compression effects of the real refractive index profile and the gain-or-loss distribution are produced. PubDate: Sun, 14 Oct 2018 00:00:00 +000

Abstract: A new theoretical approach has been established to define transport coefficients of charge and mass transport in porous materials directly from impedance data; thus four transport coefficients could be determined. In case of ammonia adsorption on sulfated zirconia, the diffusion coefficient was figured out to be approximately the mobility diffusion coefficient of ammonium ions: 1.2 x 10-7 cm2/s. The transport of carbon dioxide was examined for samples of zeolite type 5A in different hydration states. By impedance spectroscopy measurements, the diffusion coefficient of water vapor at 373 K is estimated to be about 7 x 10-6 cm2/s. The influence of carbon dioxide adsorption on diffusion coefficients is studied based on two pellet types of zeolite 5A. The difference between polar and non-polar gas adsorption in porous solids is considered as changed characteristic of impedance. PubDate: Thu, 04 Oct 2018 06:37:48 +000

Abstract: In the present study a particular case of Gross-Pitaevskii or nonlinear Schrödinger equation is rewritten to a form similar to a hydrodynamic Euler equation using the Madelung transformation. The obtained system of differential equations is highly nonlinear. Regarding the solutions, a larger coefficient of the nonlinear term yields stronger deviation of the solution from the linear case. PubDate: Mon, 01 Oct 2018 00:00:00 +000

Abstract: The presence and propagation of dust-acoustic solitary waves in dusty plasma contains four components such as negative and positive dust species beside ions and electrons are studied. Both the ions and electrons distributions are represented applying nonextensive formula. Employing the reductive perturbation method, an evolution equation is derived to describe the small-amplitude dust-acoustic solitons in the considered plasma system. The used reductive perturbation stretches lead to the nonlinear KdV and modified KdV equations with nonlinear and dispersion coefficients that depend on the parameters of the plasma. This study represents that the presence of compressive or/and rarefactive solitary waves depends mainly on the value of the first-order nonlinear coefficient. The structure of envelope wave is undefined for first-order nonlinear coefficient tends to vanish. The coexistence of the two types of solitary waves appears by increasing the strength of nonlinearity to the second order using the modified KdV equation. PubDate: Thu, 27 Sep 2018 07:41:22 +000

Abstract: We introduce the generalized q-deformed Sinh-Gordon equation and derive analytical soliton solutions for some sets of parameters. This new defined equation could be useful for modeling physical systems with violated symmetries. PubDate: Tue, 25 Sep 2018 10:26:54 +000

Abstract: The nonlinear phenomena which associate with magnetoacoustic waves in a plasma are analytically studied. A plasma is an open system with external inflow of energy and radiation losses. A plasma’s flow may be isentropically stable or unstable. The nonlinear phenomena occur differently in dependence on stability or instability of a plasma’s flow. The nonlinear instantaneous equation which describes dynamics of nonwave entropy mode in the field of intense magnetoacoustic perturbations is the result of special projecting of the conservation equations in the differential form. It is analyzed in some physically meaningful cases; those are periodic magnetoacoustic perturbations and particular cases of heating-cooling function. A plasma is situated in the straight magnetic field with constant equilibrium magnetic strength which form constant angle with the direction of wave propagation. A plasma is initially uniform and equilibrium. The conclusions concern nonlinear effects of fast and slow magnetoacoustic perturbations and may be useful in direct and inverse problems. PubDate: Mon, 24 Sep 2018 00:00:00 +000

Abstract: We study representations of Hom-Lie algebroids, give some properties of Hom-Lie algebroids, and discuss equivalent statements of Hom-Lie algebroids. Then, we prove that two known definitions of Hom-Lie algebroids can be transformed into each other under some conditions. PubDate: Wed, 19 Sep 2018 08:06:28 +000

Abstract: A two-parameter autonomous jerk oscillator with a cosine hyperbolic nonlinearity is proposed in this paper. Firstly, the stability of equilibrium points of proposed autonomous jerk oscillator is investigated by analyzing the characteristic equation and the existence of Hopf bifurcation is verified using one of the two parameters as a bifurcation parameter. By tuning its two parameters, various dynamical behaviors are found in the proposed autonomous jerk oscillator including periodic attractor, one-scroll chaotic attractor, and coexistence between chaotic and periodic attractors. The proposed autonomous jerk oscillator has period-doubling route to chaos with the variation of one of its parameters and reverse period-doubling route to chaos with the variation of its other parameter. The proposed autonomous jerk oscillator is modelled on Field Programmable Gate Array (FPGA) and the FPGA chip statistics and phase portraits are derived. The chaotic and coexistence of attractors generated in the proposed autonomous jerk oscillator are confirmed by FPGA implementation of the proposed autonomous jerk oscillator. A good qualitative agreement is illustrated between the numerical and FPGA results. Finally synchronization of unidirectional coupled identical proposed autonomous jerk oscillators is achieved using adaptive sliding mode control method. PubDate: Mon, 17 Sep 2018 06:54:20 +000

Abstract: Approximate symmetries, which are admitted by the perturbed KdV equation, are obtained. The optimal system of one-dimensional subalgebra of symmetry algebra is obtained. The approximate invariants of the presented approximate symmetries and some new approximately invariant solutions to the equation are constructed. Moreover, the conservation laws have been constructed by using partial Lagrangian method. PubDate: Sun, 09 Sep 2018 00:00:00 +000

Abstract: We present the dimensional regularization approach to the renormalization group theory of the generalized sine-Gordon model. The generalized sine-Gordon model means the sine-Gordon model with high frequency cosine modes. We derive renormalization group equations for the generalized sine-Gordon model by regularizing the divergence based on the dimensional method. We discuss the scaling property of renormalization group equations. The generalized model would present a new class of scaling property. PubDate: Thu, 06 Sep 2018 06:34:51 +000

Abstract: In this paper, we study the perturbed Riemann problem with delta shock for a hyperbolic system. The problem is different from the previous perturbed Riemann problems which have no delta shock. The solutions to the problem are obtained constructively. From the solutions, we see that a delta shock in the corresponding Riemann solution may turn into a shock and a contact discontinuity under a perturbation of the Riemann initial data. This shows the instability and the internal mechanism of a delta shock. Furthermore, we find that the Riemann solution of the hyperbolic system is instable under this perturbation, which is also quite different from the previous perturbed Riemann problems. PubDate: Wed, 05 Sep 2018 07:25:42 +000

Abstract: We generalize Calabi-Yau’s linear volume growth theorem to Finsler manifold with the weighted Ricci curvature bounded below by a negative function and show that such a manifold must have infinite volume. PubDate: Sun, 02 Sep 2018 00:00:00 +000

Abstract: We study a type of iterative method and apply it to time-fractional Swift-Hohenberg equation with initial value. Using this iterative method, we obtain the approximate analytic solutions with numerical figures to initial value problems, which indicates that such iterative method is effective and simple in constructing approximate solutions to Cauchy problems of time-fractional differential equations. PubDate: Sun, 02 Sep 2018 00:00:00 +000

Abstract: Non-Hermitian quantum physics is used successfully for the description of different puzzling experimental results, which are observed in open quantum systems. Mostly, the influence of exceptional points on the dynamical properties of the system is studied. At these points, two complex eigenvalues of the non-Hermitian Hamiltonian coalesce (where is the energy and is the inverse lifetime of the state ). We show that also the eigenfunctions of the two states play an important role, sometimes even the dominant one. Besides exceptional points, other critical points exist in non-Hermitian quantum physics. At these points in the parameter space, the biorthogonal eigenfunctions of become orthogonal. For illustration, we show characteristic numerical results. PubDate: Sun, 02 Sep 2018 00:00:00 +000

Abstract: The dynamical symmetries of -dimensional Matrix Partial Differential Equations with a Calogero potential (with/without the presence of an extra oscillatorial de Alfaro-Fubini-Furlan, DFF, term) are investigated. The first-order invariant differential operators induce several invariant algebras and superalgebras. Besides the invariance of the Calogero Conformal Mechanics, an invariant superalgebra, realized by first-order and second-order differential operators, is obtained. The invariant algebras with an infinite tower of generators are given by the universal enveloping algebra of the deformed Heisenberg algebra, which is shown to be equivalent to a deformed version of the Schrödinger algebra. This vector space also gives rise to a higher-spin (gravity) superalgebra. We furthermore prove that the pure and DFF Matrix Calogero PDEs possess isomorphic dynamical symmetries, being related by a similarity transformation and a redefinition of the time variable. PubDate: Sun, 02 Sep 2018 00:00:00 +000

Abstract: We investigate the influence of the surface effects on a diffusive process by considering that the particles may be sorbed or desorbed or undergo a reaction process on the surface with the production of a different substance. Our analysis considers a semi-infinite medium, where the particles may diffuse in contact with a surface with active sites. For the surface effects, we consider integrodifferential boundary conditions coupled with a kinetic equation which takes non-Debye relation process into account, allowing the analysis of a broad class of processes. We also consider the presence of the fractional derivatives in the bulk equations. In this scenario, we obtain solutions for the particles in the bulk and on the surface. PubDate: Thu, 09 Aug 2018 07:34:10 +000

Abstract: The traditional (G/G2) expansion method is modified to extend the symmetric extension to the negative power term in the solution to the positive power term. The general traveling wave solution is extended to a generalized solution that can separate variables. By using this method, the solution to the detached variables of the symmetric extended form of the 2+1-dimensional NNV equation can be solved, also the soliton structure and fractal structure of Dromion can be studied well. PubDate: Thu, 09 Aug 2018 07:29:54 +000

Abstract: Consider the following nonlocal integrodifferential system: , where is a general nonlocal integrodifferential operator, , is a fractional Sobolev critical exponent, , , is a lower order perturbation of the critical coupling term, and is an open bounded domain in with Lipschitz boundary. Under proper conditions, we establish an existence result of the ground state solution to the nonlocal integrodifferential system. PubDate: Wed, 08 Aug 2018 07:33:30 +000

Abstract: In this paper, an auxiliary equation method is introduced for seeking exact solutions expressed in variable coefficient function forms for fractional partial differential equations, where the concerned fractional derivative is defined by the conformable fractional derivative. By the use of certain fractional transformation, the fractional derivative in the equations can be converted into integer order case with respect to a new variable. As for applications, we apply this method to the time fractional two-dimensional Boussinesq equation and the space-time fractional (2+1)-dimensional breaking soliton equation. As a result, some exact solutions including variable coefficient function solutions as well as solitary wave solutions for the two equations are found. PubDate: Sun, 05 Aug 2018 00:00:00 +000

Abstract: An adjoint method of data assimilation with the characteristic finite difference (CFD) scheme is applied to marine pollutant transport problems and the temporal and spatial distribution of marine pollutants are simulated. Numerical tests of two-dimensional problems of pollutant transport with two different schemes indicate that the error of CFD is smaller than that of central difference scheme (CDS). Then the inversion experiments of the initial field and the source and sink terms of pollutants are carried out. Applying CFD in the adjoint method of data assimilation cannot only reduce simulation error to get a good inversion but can also enable larger time step size to decrease computation time and improve the calculation efficiency. PubDate: Thu, 02 Aug 2018 09:21:59 +000

Abstract: In this paper, we study a nonlinear system involving the fractional p-Laplacian in a unit ball and establish the radial symmetry and monotonicity of its positive solutions. By using the direct method of moving planes, we prove the following result. For , if and satisfy the following nonlinear system and are nonnegative continuous functions satisfying the following: (i) and are increasing for ; (ii) , are bounded near . Then the positive solutions must be radially symmetric and monotone decreasing about the origin. PubDate: Wed, 01 Aug 2018 00:00:00 +000

Abstract: We construct solutions to the Johnson equation (J) first by means of Fredholm determinants and then by means of Wronskians of order giving solutions of order depending on parameters. We obtain order rational solutions that can be written as a quotient of two polynomials of degree in , and in depending on parameters. This method gives an infinite hierarchy of solutions to the Johnson equation. In particular, rational solutions are obtained. The solutions of order with parameters are constructed and studied in detail by means of their modulus in the plane in function of time and parameters ,,, and . PubDate: Wed, 01 Aug 2018 00:00:00 +000

Abstract: Based on projective synchronization and combination synchronization model, a type of combination-combination projective synchronization is realized via nonsingular sliding mode control technique for multiple different chaotic systems. Concretely, on the basic of the adaptive laws and stability theory, the corresponding sliding mode control surfaces and controllers are designed to achieve the combination-combination projective synchronization between the combination of two chaotic systems as drive system and the combination of multiple chaotic systems as response system with disturbances. Some criteria and corollaries are derived for combination-combination projective synchronization of the multiple different chaotic systems. Finally, the numerical simulation results are presented to demonstrate the effectiveness and correctness of the synchronization scheme. PubDate: Wed, 01 Aug 2018 00:00:00 +000

Abstract: It is shown that quasi-Frobenius Hom-Lie algebras are connected with a class of solutions of the classical Hom-Yang-Baxter equations. Moreover, a similar relation is discussed on Frobenius (symmetric) monoidal Hom-algebras and solutions of quantum Hom-Yang-Baxter equations. Monoidal Hom-Hopf algebras with Frobenius structures are studied at last. PubDate: Wed, 01 Aug 2018 00:00:00 +000

Abstract: This paper studies the convergence of Riemann solutions to the inhomogeneous modified Chaplygin gas equations as the pressure vanishes. The delta shock waves and vacuum states occur as the pressure vanishes. The Riemann solutions of inhomogeneous modified Chaplygin gas equations are no longer self-similar. It is obviously different from the Riemann solutions of homogeneous modified Chaplygin gas equations. When the pressure vanishes, the Riemann solutions of the modified Chaplygin gas equations with a coulomb-like friction term converge to the Riemann solutions of the pressureless Euler system with a source term. PubDate: Wed, 01 Aug 2018 00:00:00 +000

Abstract: We focus on the nonexistence of global weak solutions of nonlinear Keldysh type equation with one derivative term. In terms of the analysis of the first Fourier coefficient, we show the solution of singular initial value problem and singular initial-boundary value problem of the nonlinear equation with positive initial data blow-up in some finite time interval. PubDate: Wed, 01 Aug 2018 00:00:00 +000

Abstract: The singularity solution for the inhomogeneous Landau-Lifshitz (ILL) equation without damping term in -dimensional space was investigated. The implicit singularity solution was obtained for the case where the target space is on . This solution can be classified into four types that cover the global and local solutions. An estimation of the energy density of one of these types indicates its exact decay rate, which allows a global solution with finite initial energy under . Analysis of the four aperiodic solutions indicates that energy gaps that are first contributions to the literature of ILL will occur for particular coefficient settings, and these are shown graphically. PubDate: Wed, 01 Aug 2018 00:00:00 +000

Abstract: A simple link between matrices of the Duffin-Kemmer-Petiau theory and matrices of Tzou representations is constructed. The link consists of a constant unitary transformation of the matrices and a projection onto a lower-dimensional subspace. PubDate: Sun, 22 Jul 2018 06:47:48 +000

Abstract: This paper deals with a mathematical fluid-particle interaction model used to describing the evolution of particles dispersed in a viscous compressible non-Newtonian fluid. It is proved that the initial boundary value problems with vacuum admits a unique local strong solution in the dimensional case. The strong nonlinearity of the system brings us difficulties due to the fact that the viscosity term and non-Newtonian gravitational potential term are fully nonlinear. PubDate: Tue, 17 Jul 2018 00:00:00 +000