查看更多>>摘要：Let lambda, lambda' be a pair of closed Legendrian submanifolds in a closed contact manifold (Y, xi = Ker(alpha)) related by a Legendrian cobordism W subset of & nbsp;& nbsp;& nbsp;(C x Y, xi tilde = Ker(-yd.x +alpha)). In this note, we show that in the hypertight setting, if A intersects for reasons of Floer homology a closed pre-Lagrangian P subset of & nbsp;& nbsp;Y which is either weakly exact or monotone, then so does lambda'. (C)& nbsp;2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：We show that any left invariant metric with harmonic curvature on a solvable Lie group is Ricci-parallel. We show the same result for any Lie group of dimension & nbsp; <= 6. (C) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：We study transversely metaplectic structures and transversely symplectic Dirac operators on transversely symplectic foliations.& nbsp; And we give the Weitzenbock type formula for transversely symplectic Dirac operators.& nbsp; Moreover, we estimate the lower bound of the eigenvalues of the transversely symplectic Dirac operator defined by the transverse Levi-Civita connection on transverse K & auml;hler foliations.
查看更多>>摘要：We generalize the F-K invariant, i.e. (Z) over cap for the complement of a knot Kin the 3-sphere, the knots-quivers correspondence, and A-polynomials of knots, and find several interconnections between them. We associate an F-K invariant to any branch of the A-polynomial of K and we work out explicit expressions for several simple knots. We show that these F-K invariants can be written in the form of a quiver generating series, in analogy with the knots-quivers correspondence. We discuss various methods to obtain such quiver representations, among others using R-matrices. We generalize the quantum a-deformed A-polynomial to an ideal that contains the recursion relation in the group rank, i.e. in the parameter a, and describe its classical limit in terms of the Coulomb branch of a 3d-5d theory. We also provide t-deformed versions. Furthermore, we study how the quiver formulation for closed 3-manifolds obtained by surgery leads to the superpotential of 3d N = 2 theory T[M-3] and to the data of the associated modular tensor category MTC[M-3]. (C) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：We constructed a multi-parametric deformation of the Brauer algebra representation related with the symplectic Lie algebras. The notion of Manin matrix of type C was generalised to the case of the multi-parametric deformation by using this representation and corresponding quadratic algebras. We derived pairing operators for these quadratic algebras and minors for the considered Manin matrices. The rank of pairing operators and dimensions of components of quadratic algebras were calculated. (c) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：The dynamics of solitons waves associated with higher-order nonlinear partial differential equations that model situations in physical systems obtainable in the fields of science and engineering help to understand the physical meaning of various soliton solutions obtained for these nonlinear differential equations. Thus, in this paper, we analytically investigate an extended Kadomtsev-Petviashvili-like equation existent in three dimensions. The robust technique of the Lie group theory of differential equation was invoked to achieve analytic solutions to the equation. This technique is used in a systematic way to generate the Lie point symmetries of the equation under study. Consequently, an optimal system of Lie subalgebra related to the equation is obtained. Thereafter, we engage the various gained subalgebras to reduce the Kadomtsev-Petviashvili-like equation to ordinary differential equations for the possibility of obtaining relevant closed-form solutions. Fortunately, various soliton solutions were found. These include different complex soliton solutions consisting of dark, bright, topological kink and singular. Some other solutions achieved are logarithmic, periodic and those which contain arbitrary functions. Therefore, to understand the physical meaning of these solutions, we depict them graphically. This exposed us to various wave structures which were later analyzed and applied. Moreover, we highlighted the significance of these solutions in various fields of science and engineering. (c) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：We conduct two nonlocal group reductions of the AKNS matrix spectral problems to generate a class of nonlocal reverse-spacetime integrable mKdV equations. One reduction replaces the spectral parameter with its negative complex conjugate while the other does not change the spectral parameter. Beginning with the specific distribution of eigenvalues, we construct soliton solutions by solving the corresponding generalized Riemann-Hilbert problems with the identity jump matrix, where eigenvalues could equal adjoint eigenvalues. (C)& nbsp;2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：In this paper we discuss physical derivations of the quantum K theory rings of symplectic Grassmannians. We compare to standard presentations in terms of Schubert cycles, but most of our work revolves around a proposed description in terms of two other bases, involving shifted Wilson lines and lambda y classes, which are motivated by and amenable to physics, and which we also provide for ordinary Grassmannians. (c) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：Three well known properties of solitons will be discussed in this paper, like Painleve test (P-test), Hirota bilinear method (HBM) and extended modified auxiliary equation mapping (EMAEM) architectonic in saturable cubic quintic nonlinear media (SCQNM) in the presence of nonlinear dispersion. The P-test will be used to examine the integrability of our governing model. For finding multiple soliton interaction HBM scheme will be adopted. EMAEM architectonic will be implemented in order to obtain some new solitary wave solutions like bright dromion (soliton), domain wall, singular, periodic, doubly periodic, trigonometric, rational and hyperbolic solutions etc. Graphical outcomes (3D, 2D, and density plots) will be shown to reflect the actual behavior of results. (c) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：We apply the (& part;)over bar-dressing method to study nonlocal modified Korteweg-de Vries (nonlocal mKdV) equation. A spatial and a time singular spectral problems associated with nonlocal mKdV equation are derived from a local 2 x 2 matrix (& part;)over bar-equation via two linear constraint equations. A nonlocal mKdV hierarchy is proposed by using recursive operator. And the conservation laws of the nonlocal mKdV are derived by the temporal linear spectral problem. The N-solitions of the nonlocal mKdV equation are constructed still based the (& part;)over bar-equation by choosing a special spectral transformation matrix. Further the explicit one- and two-soliton solutions are obtained. The results on the mKdV equation can be recovered from the conclusion given above as special reductions. (C)& nbsp;2022 Elsevier B.V. All rights reserved.
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