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Dynamics of fundamental and double-pole breathers and solitons for a nonlinear Schrodinger equation with sextic operator under non-zero boundary conditions
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作者 Luyao Zhang Xiyang Xie 《Chinese Physics B》 SCIE EI CAS CSCD 2024年第9期268-280,共13页
We study the dynamics of fundamental and double-pole breathers and solitons for the focusing and defocusing nonlinear Schrodinger equation with the sextic operator under non-zero boundary conditions. Our analysis main... We study the dynamics of fundamental and double-pole breathers and solitons for the focusing and defocusing nonlinear Schrodinger equation with the sextic operator under non-zero boundary conditions. Our analysis mainly focuses onthe dynamical properties of simple- and double-pole solutions. Firstly, through verification, we find that solutions undernon-zero boundary conditions can be transformed into solutions under zero boundary conditions, whether in simple-pole ordouble-pole cases. For the focusing case, in the investigation of simple-pole solutions, temporal periodic breather and thespatial-temporal periodic breather are obtained by modulating parameters. Additionally, in the case of multi-pole solitons,we analyze parallel-state solitons, bound-state solitons, and intersecting solitons, providing a brief analysis of their interactions.In the double-pole case, we observe that the two solitons undergo two interactions, resulting in a distinctive “triangle”crest. Furthermore, for the defocusing case, we briefly consider two situations of simple-pole solutions, obtaining one andtwo dark solitons. 展开更多
关键词 double-pole solitons double-pole breathers Riemann-Hilbert problem non-zero boundary con-ditions nonlinear Schrodinger equation with sextic operator
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Euler’s First-Order Explicit Method–Peridynamic Differential Operator for Solving Population Balance Equations of the Crystallization Process
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作者 Chunlei Ruan Cengceng Dong +2 位作者 Kunfeng Liang Zhijun Liu Xinru Bao 《Computer Modeling in Engineering & Sciences》 SCIE EI 2024年第3期3033-3049,共17页
Using Euler’s first-order explicit(EE)method and the peridynamic differential operator(PDDO)to discretize the time and internal crystal-size derivatives,respectively,the Euler’s first-order explicit method–peridyna... Using Euler’s first-order explicit(EE)method and the peridynamic differential operator(PDDO)to discretize the time and internal crystal-size derivatives,respectively,the Euler’s first-order explicit method–peridynamic differential operator(EE–PDDO)was obtained for solving the one-dimensional population balance equation in crystallization.Four different conditions during crystallization were studied:size-independent growth,sizedependent growth in a batch process,nucleation and size-independent growth,and nucleation and size-dependent growth in a continuous process.The high accuracy of the EE–PDDO method was confirmed by comparing it with the numerical results obtained using the second-order upwind and HR-van methods.The method is characterized by non-oscillation and high accuracy,especially in the discontinuous and sharp crystal size distribution.The stability of the EE–PDDO method,choice of weight function in the PDDO method,and optimal time step are also discussed. 展开更多
关键词 Population balance equation CRYSTALLIZATION peridynamic differential operator Euler’s first-order explicit method
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Semigroup of Weakly Continuous Operators Associated to a Generalized Schrödinger Equation
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作者 Yolanda Silvia Santiago Ayala 《Journal of Applied Mathematics and Physics》 2023年第4期1061-1076,共16页
In this work, we prove the existence and uniqueness of the solution of the generalized Schrödinger equation in the periodic distributional space P’. Furthermore, we prove that the solution depends continuously r... In this work, we prove the existence and uniqueness of the solution of the generalized Schrödinger equation in the periodic distributional space P’. Furthermore, we prove that the solution depends continuously respect to the initial data in P’. Introducing a family of weakly continuous operators, we prove that this family is a semigroup of operators in P’. Then, with this family of operators, we get a fine version of the existence and dependency continuous theorem obtained. Finally, we provide some consequences of this study. 展开更多
关键词 Semigroups Theory Weakly Continuous operators Existence of Solution Generalized Schrödinger equation Distributional Problem Periodic Distributional Space
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Iterative Solution for Systems of Binary Non-mixed Monotone Operator Equations 被引量:2
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作者 左秀会 《Chinese Quarterly Journal of Mathematics》 CSCD 2001年第3期80-83,共4页
With using the cone and partial ordering t heory and mixed monotone operator theory, the existence and uniqueness for solut ion of systems of non-monotone binary nonliear operator equations are discussed. And the it... With using the cone and partial ordering t heory and mixed monotone operator theory, the existence and uniqueness for solut ion of systems of non-monotone binary nonliear operator equations are discussed. And the iterative sequences which converge to solution of systems of operator e quations and the error estimates are also given. Some corresponding results for the mixed monotone operations and the unary operator equations are improved and generalized. 展开更多
关键词 binary operator mixed monotone operators syste ms of equations SOLUTIONS cone and partial ordering
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GLOBAL BOUND ON THE GRADIENT OF SOLUTIONS TO p-LAPLACE TYPE EQUATIONS WITH MIXED DATA
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作者 Minh-Phuong TRAN The-Quang TRAN Thanh-Nhan NGUYEN 《Acta Mathematica Scientia》 SCIE CSCD 2024年第4期1394-1414,共21页
In this paper,the study of gradient regularity for solutions of a class of elliptic problems of p-Laplace type is offered.In particular,we prove a global result concerning Lorentz-Morrey regularity of the non-homogene... In this paper,the study of gradient regularity for solutions of a class of elliptic problems of p-Laplace type is offered.In particular,we prove a global result concerning Lorentz-Morrey regularity of the non-homogeneous boundary data problem:-div((s^(2)+|▽u|^(2)p-2/2)▽u)=-div(|f|^(p-2)f)+g inΩ,u=h in■Ω,with the(sub-elliptic)degeneracy condition s∈[0,1]and with mixed data f∈L^(p)(Q;R^(n)),g∈Lp/(p-1)(Ω;R^(n))for p∈(1,n).This problem naturally arises in various applications such as dynamics of non-Newtonian fluid theory,electro-rheology,radiation of heat,plastic moulding and many others.Building on the idea of level-set inequality on fractional maximal distribution functions,it enables us to carry out a global regularity result of the solution via fractional maximal operators.Due to the significance of M_(α)and its relation with Riesz potential,estimates via fractional maximal functions allow us to bound oscillations not only for solution but also its fractional derivatives of orderα.Our approach therefore has its own interest. 展开更多
关键词 gradient estimates p-Laplace quasilinear elliptic equation fractional maximal operators Lorentz-Morrey spaces
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Propagation and Pinning of Travelling Wave for Nagumo Type Equation
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作者 Sharon-Yasotha Veerayah-Mcgregor Valipuram Manoranjan 《Journal of Applied Mathematics and Physics》 2024年第3期861-869,共9页
In this paper, we study the propagation and its failure to propagate (pinning) of a travelling wave in a Nagumo type equation, an equation that describes impulse propagation in nerve axons that also models population ... In this paper, we study the propagation and its failure to propagate (pinning) of a travelling wave in a Nagumo type equation, an equation that describes impulse propagation in nerve axons that also models population growth with Allee effect. An analytical solution is derived for the traveling wave and the work is extended to a discrete formulation with a piecewise linear reaction function. We propose an operator splitting numerical scheme to solve the equation and demonstrate that the wave either propagates or gets pinned based on how the spatial mesh is chosen. 展开更多
关键词 operator Splitting Travelling Wave Piecewise Reaction Nagumo equation PINNING Finite Differences
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INTERIOR ESTIMATES IN MORREY SPACES FOR SOLUTIONS OF ELLIPTIC EQUATIONS AND WEIGHTED BOUNDEDNESS FOR COMMUTATORS OF SINGULAR INTEGRAL OPERATORS 被引量:14
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作者 刘岚喆 《Acta Mathematica Scientia》 SCIE CSCD 2005年第1期89-94,共6页
It is proved that, for the nondivergence elliptic equations Σi,jn=1aijuxixj=f, if f belongs to the generalized Morrey spaces Lp, (w), then uxixj ∈ Lp, (w), where u is the W2,p-solution of the equations. In order to ... It is proved that, for the nondivergence elliptic equations Σi,jn=1aijuxixj=f, if f belongs to the generalized Morrey spaces Lp, (w), then uxixj ∈ Lp, (w), where u is the W2,p-solution of the equations. In order to obtain this, the author first establish the weighted boundedness for the commutators of some singular integral operators on Lp, (w). 展开更多
关键词 Nondivergence elliptic equation generalized Morrey space commutator of singular integral operator Ap weight
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ON THE EXISTENCE AND UNIQUENESS THEOREMS OF SOLUTIONS FOR THE SYSTEMS OF MIXED MONOTONE OPERATOR EQUATIONS WITH APPLICATIONS 被引量:11
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作者 张石生 郭伟平 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 1993年第1期1-14,共14页
The existence, uniqueness and non-symmetric iterative approximation of solutions for a class of systems of mixed monotone operator equations are discussed. As an application, we utilize, the results presented in this ... The existence, uniqueness and non-symmetric iterative approximation of solutions for a class of systems of mixed monotone operator equations are discussed. As an application, we utilize, the results presented in this paper to study the existence and uniqueness problems of common solutions for a class of systems of functional equations arising in dynamic programming of multistage decision processes and a class of systems of nonlinear integral equation. The results obtained in this paper not only answer an open question suggested in [3] but also generalize the corresponding results of [1],[2]. 展开更多
关键词 Mixed Monotone operator Non-symmetric Iteration System of Functional equations
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Iterative Solutions for a Non-monotone BinaryOperator Equations and Operator System of Equations 被引量:9
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作者 ZHANGFei-ran ZHOUXiao-zhong 《Chinese Quarterly Journal of Mathematics》 CSCD 2004年第1期69-74,共6页
By using the theory of the cone and partial ordering. It is studied that the existence and uniqueness of solutions for a non-monotone binary operator equation A(x, x)= x and operator system of equations A(x,x)=x,B(x,x... By using the theory of the cone and partial ordering. It is studied that the existence and uniqueness of solutions for a non-monotone binary operator equation A(x, x)= x and operator system of equations A(x,x)=x,B(x,x)=x in Banach spaces. Where A and B can be decomposed A=A1+A2, B=B1+B2,A1 and B1 are mixed monotone, A2 and B2 are anti-mixed monotone. The results presented here improve and generalize some corresponding results of mixed monotone operator equations. 展开更多
关键词 cone and partial ordering operator equations anti-mixed monotone
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ITERATIVE REGULARIZATION METHODS FOR NONLINEAR ILL-POSED OPERATOR EQUATIONS WITH M-ACCRETIVE MAPPINGS IN BANACH SPACES 被引量:2
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作者 Ioannis K.ARGYROS Santhosh GEORGE 《Acta Mathematica Scientia》 SCIE CSCD 2015年第6期1318-1324,共7页
In this paper, a modified Newton type iterative method is considered for ap- proximately solving ill-posed nonlinear operator equations involving m-accretive mappings in Banach space. Convergence rate of the method is... In this paper, a modified Newton type iterative method is considered for ap- proximately solving ill-posed nonlinear operator equations involving m-accretive mappings in Banach space. Convergence rate of the method is obtained based on an a priori choice of the regularization parameter. Our analysis is not based on the sequential continuity of the normalized duality mapping. 展开更多
关键词 nonlinear ill-posed equations iterative regularization m-accretive operator Newton type method
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Operator Fredholm Integration Equation in Intermediate Coordinate-Momentum Representation and Its Analogue to Thermo Conduction Equation 被引量:2
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作者 FAN Hong-Yi TANG Xu-Bing 《Communications in Theoretical Physics》 SCIE CAS CSCD 2008年第5期1169-1172,共4页
Using the technique of integration within an ordered product (IWOP) of operators we construct intermediate coordinate-momentum representation, with which we build a type of operator Fredholm integration equation tha... Using the technique of integration within an ordered product (IWOP) of operators we construct intermediate coordinate-momentum representation, with which we build a type of operator Fredholm integration equation that is an operator generalization of the solution of thermo conduction equation. Then we seach for the solution of operator Fredholm integration equations, which provides us with a new approach for deriving some operator identities. 展开更多
关键词 operator Fredholm equation intermediate coordinate-momentum representation thermo conduction equation
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ITERATIVE SOLUTIONS FOR SYSTEMS OF NONLINEAR OPERATOR EQUATIONS IN BANACH SPACE 被引量:1
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作者 宋光兴 《Acta Mathematica Scientia》 SCIE CSCD 2003年第4期461-466,共6页
By using partial order method, the existence, uniqueness and iterative approximation of solutions for a class of systems of nonlinear operator equations in Banach space are discussed. The results obtained in this pape... By using partial order method, the existence, uniqueness and iterative approximation of solutions for a class of systems of nonlinear operator equations in Banach space are discussed. The results obtained in this paper extend and improve recent results. 展开更多
关键词 System of operator equations SOLUTION iterative technique cone and partial ordering banach space
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Invertibility of Infinite-Dimensional Hamiltonian Operators and Its Application to Plate Bending Equation 被引量:2
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作者 Alatancang 《Communications in Theoretical Physics》 SCIE CAS CSCD 2008年第3期562-566,共5页
The results of invertibility and spectrum for some different classes of infinite-dimensional Hayniltonian operators, after a brief classification by domains. are given. By the above results, the associated infinite-di... The results of invertibility and spectrum for some different classes of infinite-dimensional Hayniltonian operators, after a brief classification by domains. are given. By the above results, the associated infinite-dimensional Hamiltonian operator with simple supported rectangular plate is proved to be invertible. Furthermore, by a certain compactness, we find that the spectrum of this operator consists only of isolated eigenvalues with finite geometric multiplicity, which will play a significant role in finding the analytical and numerical solution based on Hamiltonian system for a class of plate bending equations. 展开更多
关键词 vplate bending equation INVERTIBILITY infinite-dimensional Hamiltonian operator
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ON SOME BOUNDARY VALUE PROBLEMS FOR NONHOMOGENOUS POLYHARMONIC EQUATION WITH BOUNDARY OPERATORS OF FRACTIONAL ORDER 被引量:1
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作者 Batirkhan TURMETOV 《Acta Mathematica Scientia》 SCIE CSCD 2016年第3期831-846,共16页
In the paper we study questions about solvability of some boundary value prob- lems for a non-homogenous poly-harmonic equation. As a boundary operator we consider differentiation operator of fractional order in Mille... In the paper we study questions about solvability of some boundary value prob- lems for a non-homogenous poly-harmonic equation. As a boundary operator we consider differentiation operator of fractional order in Miller-Ross sense. The considered problem is a generalization of well-known Dirichlet and Neumann problems. 展开更多
关键词 polyharmonic equation boundary value problem Dirichlet problem Neumann problem fractional derivative Miller-Ross operator
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Rota-Baxter Operators on 3-dimensional Lie Algebras and Solutions of the Classical Yang-Baxter Equation 被引量:1
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作者 Cheng Yong-sheng Wu Lin-li +1 位作者 Wang Pan-yin Du Xian-kun 《Communications in Mathematical Research》 CSCD 2019年第1期81-96,共16页
In this paper,we compute Rota-Baxter operators on the 3-dimensional Lie algebra g whose derived algebra’s dimension is 2.Furthermore,we give the corresponding solutions of the classical Yang-Baxter equation in the 6-... In this paper,we compute Rota-Baxter operators on the 3-dimensional Lie algebra g whose derived algebra’s dimension is 2.Furthermore,we give the corresponding solutions of the classical Yang-Baxter equation in the 6-dimensional Lie algebras g ■ _(ad~*) g~* and some new structures of left-symmetric algebra induced from g and its Rota-Baxter operators. 展开更多
关键词 Rota-Baxter operatorS 3-dimensional Lie ALGEBRA classical Yang-Baxter equation left-symmetric ALGEBRA
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Iterative Solution for Systems of Nonlinear Two Binary Operator Equations 被引量:2
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作者 ZHANGZhi-hong LIWen-feng 《Chinese Quarterly Journal of Mathematics》 CSCD 2004年第3期262-266,共5页
Using the cone and partial ordering theory and mixed monotone operator theory, the existence and uniqueness of solutions for some classes of systems of nonlinear two binary operator equations in a Banach space with a ... Using the cone and partial ordering theory and mixed monotone operator theory, the existence and uniqueness of solutions for some classes of systems of nonlinear two binary operator equations in a Banach space with a partial ordering are discussed. And the error estimates that the iterative sequences converge to solutions are also given. Some relevant results of solvability of two binary operator equations and systems of operator equations are improved and generalized. 展开更多
关键词 Banach spaces two binary operators systems of operator equations iterative solution
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The Solution of Binary Nonlinear Operator Equations with Applications 被引量:1
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作者 Baomin Qiao 《Applied Mathematics》 2013年第9期1237-1241,共5页
In this paper, the existence and uniqueness of solution systems for some binary nonlinear operator equations are discussed by using cone and partially order theory and monotone iteration theory, and the iterative sequ... In this paper, the existence and uniqueness of solution systems for some binary nonlinear operator equations are discussed by using cone and partially order theory and monotone iteration theory, and the iterative sequences which converge to solution of operator equations and error estimates for iterative sequences are also given. Some corresponding results are improved and generalized. Finally, the applications of our results are given. 展开更多
关键词 CONE and PARTIAL Order SOLUTION Nonlinear BINARY operator operator equationS
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Exact Inverse Operator on Field Equations 被引量:2
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作者 Edwin Eugene Klingman 《Journal of Applied Mathematics and Physics》 2020年第10期2213-2222,共10页
Differential equations of electromagnetic and similar physical fields are generally solved via antiderivative Green’s functions involving integration over a region and its boundary. Research on the Kasner metric reve... Differential equations of electromagnetic and similar physical fields are generally solved via antiderivative Green’s functions involving integration over a region and its boundary. Research on the Kasner metric reveals a variable boundary deemed inappropriate for standard anti-derivatives, suggesting the need for an alternative solution technique. In this work I derive such a solution and prove its existence, based on circulation equations in which the curl of the field is induced by source current density and possibly changes in associated fields. We present an anti-curl operator that is believed novel and we prove that it solves for the field without integration required. 展开更多
关键词 Anti-Derivative Anti-Curl operator Maxwell’s equations Geometric Calculus Kasner Metric Green’s Function Biot-Savart operator
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Multilevel Iteration Methods for Solving Linear Operator Equations of the First Kind 被引量:2
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作者 罗兴钧 《Northeastern Mathematical Journal》 CSCD 2008年第1期1-9,共9页
In this paper we develop two multilevel iteration methods for solving linear systems resulting from the Galerkin method and Tikhonov regularization for linear ill-posed problems. The two algorithms and their convergen... In this paper we develop two multilevel iteration methods for solving linear systems resulting from the Galerkin method and Tikhonov regularization for linear ill-posed problems. The two algorithms and their convergence analyses are presented in an abstract framework. 展开更多
关键词 operator equations of the first kind ill-posed problem multilevel iteration method Tikhonov regularization
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Pseudo-differential Operators and Generalized Lax Equations in Symbolic Computation 被引量:1
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作者 JIA Yi-Feng CHEN Yu-Fu 《Communications in Theoretical Physics》 SCIE CAS CSCD 2008年第5期1139-1144,共6页
In this paper, the pseudo-differential operators and the generalized Lax equations in integrable systems are implemented in symbolic software Mathematica. A great deal of differential polynomials which appear in the p... In this paper, the pseudo-differential operators and the generalized Lax equations in integrable systems are implemented in symbolic software Mathematica. A great deal of differential polynomials which appear in the procedure are dealt with by differential characteristic chain method. Using the program, several classical examples are given. 展开更多
关键词 pseudo-differential operators generalized Lax equation Zakharov-Shabat equation integral systems HIERARCHY characteristic chain
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