Article
Mathematics, Applied
Wen-Xiu Ma
Summary: This paper presents nonlocal reverse-spacetime PT-symmetric multicomponent nonlinear Schrodinger equations and their inverse scattering transforms and soliton solutions using the Riemann-Hilbert technique under a specific nonlocal group reduction. The Sokhotski-Plemelj formula is used to determine solutions to a class of associated Riemann-Hilbert problems and transform the systems that generalized Jost solutions need to satisfy. A formulation of solutions is developed for the Riemann-Hilbert problems associated with the reflectionless transforms, and soliton solutions are constructed for the presented nonlocal reverse-spacetime PT-symmetric NLS equations.
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
(2021)
Article
Mathematics, Applied
Wen-Xiu Ma
Summary: This study proposes a nonlocal real reverse-spacetime integrable hierarchies of PT symmetric matrix AKNS equations, achieved through nonlocal symmetry reductions on the potential matrix, to determine generalized Jost solutions. By applying the Sokhotski-Plemelj formula, the associated Riemann-Hilbert problems are transformed into integral equations of Gelfand-Levitan-Marchenko type. The Riemann-Hilbert problems corresponding to the reflectionless case are explicitly solved, presenting soliton solutions for the resulting nonlocal real reverse-spacetime integrable PT-symmetric matrix AKNS equations.
PHYSICA D-NONLINEAR PHENOMENA
(2022)
Article
Multidisciplinary Sciences
Liming Ling, Wen-Xiu Ma
Summary: This paper investigates the soliton solutions of nonlocal complex reverse-spacetime mKdV hierarchies through nonlocal symmetry reductions of matrix spectral problems. By formulating the corresponding inverse scattering problems and constructing solutions to specific Riemann-Hilbert problems, N-soliton solutions to the hierarchies are obtained.
Article
Physics, Multidisciplinary
Wen-Xiu Ma
Summary: In this paper, a class of novel reduced nonlocal reverse-spacetime integrable modified Korteweg-de Vries equations is presented through two group reductions of the Ablowitz-Kaup-Newell-Segur matrix spectral problems. Soliton solutions are generated from the reflectionless Riemann-Hilbert problems by taking advantage of the distribution of eigenvalues, where eigenvalues could equal adjoint eigenvalues.
COMMUNICATIONS IN THEORETICAL PHYSICS
(2022)
Article
Engineering, Mechanical
Wen-Xin Zhang, Yaqing Liu, Xin Chen, Shijie Zeng
Summary: The main focus of this paper is to investigate the soliton solutions and asymptotic behavior of the integrable reverse space-time nonlocal Sasa-Satsuma equation, derived from a coupled two-component Sasa-Satsuma system with a specific constraint. The soliton solutions are obtained by solving the inverse scattering problems using the Riemann-Hilbert method. The reverse space-time nonlocal Sasa-Satsuma equation exhibits novel symmetries and constraints in the discrete eigenvalues and eigenvectors, compared to local systems. The obtained results on the soliton solutions and their dynamics, as well as the asymptotic behaviors, contribute to a better understanding of nonlocal nonlinear systems.
NONLINEAR DYNAMICS
(2023)
Article
Engineering, Mechanical
Jianping Wu
Summary: In this paper, a novel general nonlocal reversed-time nonlinear Schrodinger equation is proposed from a general coupled NLS system by imposing a nonlocal reversed-time constraint. The equation describes the nonlinear wave propagations where the components of the coupled NLS system are related by the nonlocal reversed-time constraint. Soliton solutions are obtained using the Riemann-Hilbert method, and the soliton dynamical behaviors are explored and illustrated.
NONLINEAR DYNAMICS
(2023)
Article
Mathematics
Wenxiu Ma
Summary: This paper focuses on establishing Riemann-Hilbert problems and presenting soliton solutions for nonlocal reverse-time nonlinear Schrodinger (NLS) hierarchies associated with higher-order matrix spectral problems. The Sokhotski-Plemelj formula is used to transform the Riemann-Hilbert problems into Gelfand-Levitan-Marchenko type integral equations. A new formulation of solutions to special Riemann-Hilbert problems with the identity jump matrix, corresponding to the reflectionless inverse scattering transforms, is proposed and applied to construction of soliton solutions to each system in the considered nonlocal reverse-time NLS hierarchies.
ACTA MATHEMATICA SCIENTIA
(2022)
Article
Mathematics, Applied
Wen-Xiu Ma
Summary: Two nonlocal group reductions were used to generate a class of nonlocal reverse-spacetime integrable mKdV equations from the AKNS matrix spectral problems, leading to soliton solutions through solving corresponding generalized Riemann-Hilbert problems with the identity jump matrix.
JOURNAL OF GEOMETRY AND PHYSICS
(2022)
Article
Mathematics, Applied
Wen-Xiu Ma
Summary: A novel reduced nonlocal integrable mKdV equation of odd order is presented by taking two group reductions of the AKNS matrix spectral problems. Soliton solutions are generated from the corresponding reflectionless Riemann-Hilbert problems based on the distribution of eigenvalues.
APPLIED MATHEMATICS LETTERS
(2022)
Article
Engineering, Mechanical
Jianping Wu
Summary: The paper presents a Riemann-Hilbert (RH) approach for a physically meaningful nonlocal integrable nonlinear Schrodinger equation of reverse-time type. The obtained results include symmetry relations of the scattering data, general multi-soliton solutions in reflectionless cases, and long-time behaviors of solutions in reflection cases. Furthermore, special soliton dynamics are explored and illustrated using Mathematica, demonstrating the remarkable features of the obtained multi-soliton solutions.
NONLINEAR DYNAMICS
(2022)
Article
Mathematics, Applied
Leilei Liu, Weiguo Zhang
Summary: The study focuses on the Cauchy problem for the integrable nonlocal modified KdV equation, constructing the solution through solving a 2 x 2 matrix Riemann-Hilbert problem in the complex plane. Additionally, an explicit form of the one-soliton solution is presented in terms of the Riemann-Hilbert problem.
APPLIED MATHEMATICS LETTERS
(2021)
Article
Mathematics, Applied
Yong Zhang, Huan-He Dong
Summary: In this paper, a multi-component nonlocal reverse-time GI equation is derived based on the zero curvature equation through nonlocal group reduction. Soliton solutions of this new equation are obtained using the Riemann-Hilbert problem, with N-soliton solutions under the reflectless case and solutions determined by the Sokhotski-Plemelj formula when the jump is not an identity.
APPLIED MATHEMATICS LETTERS
(2022)
Article
Physics, Multidisciplinary
Wen-Xiu Ma
Summary: In this paper, we investigate matrix integrable fifth-order mKdV equations using a kind of group reductions of the Ablowitz-Kaup-Newell-Segur matrix spectral problems. By utilizing properties of eigenvalue and adjoint eigenvalue problems, we solve the corresponding Riemann-Hilbert problems, where eigenvalues could be equal to adjoint eigenvalues, and construct their soliton solutions, under the condition of zero reflection coefficients. Illustrative examples of scalar and two-component integrable fifth-order mKdV equations are provided.
Article
Physics, Mathematical
Wen-Xiu Ma
Summary: The paper aims to generate nonlocal integrable nonlinear Schrodinger hierarchies of type (-lambda, lambda) by imposing two nonlocal matrix restrictions of the AKNS matrix characteristic-value problems of arbitrary order. Exact soliton solutions are formulated by applying the associated reflectionless generalized Riemann-Hilbert problems based on the explored outspreading of characteristic-values and adjoint characteristic-values, in which characteristic-values and adjoint characteristic-values could have a nonempty intersection. Illustrative models of the resultant mixed-type nonlocal integrable nonlinear Schrodinger equations are presented.
INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS
(2023)
Article
Mathematics, Applied
Tongshuai Liu, Tiecheng Xia
Summary: In this paper, the multi-component generalized Gerdjikov-Ivanov integrable hierarchy is obtained using the spectral problem and zero curvature equation. The multi-Hamiltonian structures of this hierarchy are investigated using trace identity. A specific Riemann-Hilbert problem is formulated for the generalized Gerdjikov-Ivanov integrable hierarchy, and by solving this problem, N-soliton solutions can be derived.
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
(2022)
Article
Mathematics, Applied
Geunsu Choi, Mingu Jung, Sun Kwang Kim, Miguel Martin
Summary: This paper studies weak-star quasi norm attaining operators and proves that the set of such operators is dense in the space of bounded linear operators regardless of the choice of Banach spaces. It is also shown that weak-star quasi norm attaining operators have distinct properties from other types of norm attaining operators, although they may share some equivalent properties under certain conditions.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Maria Lorente, Francisco J. Martin-Reyes, Israel P. Rivera-Rios
Summary: In this paper, we provide quantitative one-sided estimates that recover the dependences in the classical setting. We estimate the one-sided maximal function in Lorentz spaces and demonstrate the applicability of the conjugation method for commutators in this context.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Fernando Cobos, Luz M. Fernandez-Cabrera
Summary: We provide a necessary and sufficient condition for the weak compactness of bilinear operators interpolated using the real method. However, this characterization does not hold for interpolated operators using the complex method.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Ovgue Gurel Yilmaz, Sofiya Ostrovska, Mehmet Turan
Summary: The Lupas q-analogue Rn,q, the first q-version of the Bernstein polynomials, was originally proposed by A. Lupas in 1987 but gained popularity 20 years later when q-analogues of classical operators in approximation theory became a focus of intensive research. This work investigates the continuity of operators Rn,q with respect to the parameter q in both the strong operator topology and the uniform operator topology, considering both fixed and infinite n.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
M. Agranovsky, A. Koldobsky, D. Ryabogin, V. Yaskin
Summary: This article modifies the concept of polynomial integrability for even dimensions and proves that ellipsoids are the only convex infinitely smooth bodies satisfying this property.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Abel Komalovics, Lajos Molnar
Summary: In this paper, a parametric family of two-variable maps on positive cones of C*-algebras is defined and studied from various perspectives. The square roots of the values of these maps under a faithful tracial positive linear functional are considered as a family of potential distance measures. The study explores the problem of well-definedness and whether these distance measures are true metrics, and also provides some related trace characterizations. Several difficult open questions are formulated.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Frederic Bayart
Summary: The passage describes the construction of an operator on a separable Hilbert space that is 5-hypercyclic for all δ in the range (ε, 1) and is not 5-hypercyclic for all δ in the range (0, ε).
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Helene Frankowska, Nikolai P. Osmolovskii
Summary: This paper investigates second-order optimality conditions for the minimization problem of a C2 function f on a general set K in a Banach space X. Both necessary and sufficient conditions are discussed, with the sufficiency condition requiring additional assumptions. The paper demonstrates the validity of these assumptions for the case when the set K is an intersection of sets described by smooth inequalities and equalities, such as in mathematical programming problems. The novelty of the approach lies in the arbitrary nature of the set K and the straightforward proofs.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Ole Fredrik Brevig, Kristian Seip
Summary: This paper studies the Hankel operator on the Hardy space and discusses its minimal and maximal norms, as well as the relationship between the maximal norm and the properties of the function.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Alexander Meskhi
Summary: Rubio de Francia's extrapolation theorem is established for new weighted grand Morrey spaces Mp),lambda,theta w (X) with weights w beyond the Muckenhoupt Ap classes. This result implies the one-weight inequality for operators of Harmonic Analysis in these spaces for appropriate weights. The necessary conditions for the boundedness of the Hardy-Littlewood maximal operator and the Hilbert transform in these spaces are also obtained. Some structural properties of new weighted grand Morrey spaces are investigated. Problems are studied in the case when operators and spaces are defined on spaces of homogeneous type.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Maud Szusterman
Summary: In this work, the necessary conditions on the structure of the boundary of a convex body K to satisfy all inequalities are investigated. A new solution for the 3-dimensional case is obtained in particular.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Rami Ayoush, Michal Wojciechowski
Summary: In this article, lower bounds for the lower Hausdorff dimension of finite measures are provided under certain restrictions on their quaternionic spherical harmonics expansions. This estimate is analogous to a result previously obtained by the authors for complex spheres.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
F. G. Abdullayev, V. V. Savchuk
Summary: This paper investigates the convergence and theorem proof of the Takenaka-Malmquist system and Fejer-type operator on the unit circle, and provides relevant results on the class of holomorphic functions representable by Cauchy-type integrals with bounded densities.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Sofiya Ostrovska, Mikhail I. Ostrovskii
Summary: This work aims to establish new results on the structure of transportation cost spaces. The main outcome of this paper states that if a metric space X contains an isometric copy of L1 in its transportation cost space, then it also contains a 1-complemented isometric copy of $1.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Pilar Rueda, Enrique A. Sanchez Perez
Summary: We prove a factorization theorem for Lipschitz operators acting on certain subsets of metric spaces of measurable functions and with values on general metric spaces. Our results show how a Lipschitz operator can be extended to a subset of other metric space of measurable functions that satisfies the following optimality condition: it is the biggest metric space, formed by measurable functions, to which the operator can be extended preserving the Lipschitz constant. Also, we demonstrate the coarsest metric that can be given for a metric space in which an order bounded lattice-valued-Lipschitz map is defined, and provide concrete examples involving the relevant space L0(mu).
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)