查看更多>>摘要：This paper's main focus is on chirped pulses (CP) for a cubic-quintic nonlinear non-paraxial pulse propagation (CQ-NNP-PP) model. Chirped solitons are a relatively new single wave phenomena. The exact CPs generate from the derivative nonlinear Schrodinger equations (NLSE). Chirp is a signal with a changing frequency over time. CPs are used in spread spectrum communications as well as some sonar and radar devices. The propagation of CPs in fibre optics is getting popular due to a wide range of applications in amplification and pulse compression. In an NLSE, the dispersion management (DM) term can influence the velocity of chirp-free nonautonomous soliton but has no effect on its shape. When there is no gain, the classical optical soliton can be expressed with a variable dispersion term and nonlinearity. DM can impact the shape and motion of non autonomous solitons for CPs. We obtain hyperbolic and periodic solutions, as well as a class of solitary wave (SW) solutions such as bright, dark, singular and bell soliton solutions. The governing model will be analyzed with the aid of Jacobian elliptic functions (JEF). We also show accomplished results in 3D and 2D structures. (C) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：In this short note, three infinite families of neutrally stable homogeneous Einstein metrics are ruled out as candidates for local maxima of the Hilbert action. (C) 2022 Elsevier B.V. All rights reserved.
Bouteraa, N.Inc, MustafaHashemi, M. S.Benaicha, S....
8页
查看更多>>摘要：The aim of the present paper is to investigate the existence and nonexistence of solutions for a nonlinear Erdelyi-Kober (EK) fractional-order differential equation associated with EK fractional integral boundary conditions on the half-line. The considered equation contains a large amount of linear and nonlinear differential equations with EK fractional operator. In order to consider this equation, we first formulated the linear problem in integral equation. Our approach is based on recent fixed point theorem which uses the strongly positive-like operators and eigenvalue criteria for existence and nonexistence of positive solutions. (C) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：We deal with the construction of covariant derivatives for some quite general Ehresmann connections on fibre bundles. We show how the introduction of a vertical endomorphism allows construction of covariant derivatives separately on both the vertical and horizontal distributions of the connection which can then be glued together on the total space. We give applications across an important class of tangent bundle cases, frame bundles and the Hopf bundle.
Wael, ShroukSeadawy, Aly R.Moawad, S. M.EL-Kalaawy, O. H....
25页
查看更多>>摘要：In this paper, the non-linear for the small long amplitude waves in two dimensional (2D) shallow water waves propagation with free surface are considered. The shallow water wave problem leads to the non-linear Hamiltonian model equation. Based on the binary Bell-polynomials approach, the bilinear form, bilinear Backlund transformation and multiple wave solutions are obtained. The conservation laws are constructed using two different techniques, namely, the Ibragimov's theorem and the multiplier method. The Noether's approach was applied to the non-linear Hamiltonian model equation to obtain the conservation laws. Also, we show that the non-linear Hamiltonian model equation is nonlinearly self-adjoint. Conserved quantities of Hamiltonian model equation are illustrated. Finally, with the help of the extended homogeneous balance method, and an exponential method, a set of new exact solutions for the non-linear Hamiltonian model equation are obtained.
查看更多>>摘要：In this paper, we study the higher Yang-Mills theory in the framework of higher gauge theory. It was shown that the 2-form electromagnetism can be generalized to the 2-form Yang-Mills theory with the group U (1) replaced by a crossed module of Lie groups. To extend this theory to even higher structure, we develop a 3-form Yang-Mills theory with a 2-crossed module of Lie groups. First, we give an explicit construction of non-degenerate symmetric G-invariant forms on the 2-crossed module of Lie algebras. Then, we derive the 3-Bianchi-Identities for 3-curvatures. Finally, we create a 3-form Yang-Mills action and obtain the corresponding field equations. (C) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：We study non-invariant Killing tensors with non-zero Nijenhuis torsion in the threedimensional Euclidean space. Generalizing the corresponding integrable systems we construct two new families of superintegrable systems in n-dimensional Euclidean space. (C) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：The curves that may have singularities on the null sphere have not been discussed before. Since they are degenerate, we can not investigate them directly. So we would like to solve these problems by using the duality theory and the results of our previous studies in Euclidean space. In addition, we discuss the evolutes and involutes of spacelike fronts and investigate their geometric properties in null sphere. Then we also give the classifications of the singularities of evolutes and involutes. Moreover, we give the dual relationships between nullcone surfaces and spacelike fronts. (C) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：In this paper, we introduce a finite Lie conformal superalgebra called the Heisenberg-Virasoro Lie conformal superalgebra s by using a class of Heisenberg-Virasoro Lie conformal modules. The super Heisenberg-Virasoro algebra of Ramond type S is defined by the formal distribution Lie superalgebra of s. Then we construct a class of simple S-modules, which are induced from simple modules of some finite dimensional solvable Lie superalgebras. These modules are isomorphic to simple restricted S-modules, and include the highest weight modules, Whittaker modules and high order Whittaker modules. As a byproduct, we present a subalgebra of S, which is isomorphic to the super Heisenberg-Virasoro algebra of Neveu-Schwarz type. (C) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：In the context of mathematical cosmology, the study of necessary and sufficient conditions for a semi-Riemannian manifold to be a (generalized) Robertson-Walker space-time is important. In particular, it is a requirement for the development of initial data to reproduce or approximate the standard cosmological model. Usually these conditions involve the Einstein field equations, which change if one considers alternative theories of gravity or if the coupling matter fields change. Therefore, the derivation of conditions which do not depend on the field equations is an advantage. In this work we present a geometric derivation of such a condition. We require the existence of a unit vector field to distinguish at each point of space two (non-equal) sectional curvatures. This is equivalent for the Riemann tensor to adopt a specific form. Our geometrical approach yields a local isometry between the space and a Robertson-Walker space of the same dimension, curvature and metric tensor sign (the dimension of the largest subspace on which the metric tensor is negative definite). Remarkably, if the space is simply-connected, the isometry is global. Our result generalizes to a class of spaces of non-constant curvature the theorem that spaces of the same constant curvature, dimension and metric tensor sign must be locally isometric. Because we do not make any assumptions regarding field equations, matter fields or metric tensor sign, one can readily use this result to study cosmological models within alternative theories of gravity or with different matter fields. (C) 2022 Elsevier B.V. All rights reserved.
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