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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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A NOTE ON PROBABILISTIC CONTRACTOR COUPLE AND SOLUTIONS FOR A SYSTEM OF NONLINEAR EQUATIONS IN N A MENGER PN-SPACES
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作者 方锦暄 宋桂安 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2000年第7期841-848,共8页
The concept of (Phi, Delta)-type probabilistic contractor couple was introduced which simplifies and weakens the definition of probabilistic contractor couple given by Zhang Shisheng. The existence and uniqueness of t... The concept of (Phi, Delta)-type probabilistic contractor couple was introduced which simplifies and weakens the definition of probabilistic contractor couple given by Zhang Shisheng. The existence and uniqueness of the solutions for a system of nonlinear operator equations with this kind of propabilistic contractor couple in N. A. Menger PN-spaces were studied. The works improve and extend the corresponding results by M. Altman, A. C. Lee, W. J. Padgett et al. 展开更多
关键词 N. A. Menger PN-space (Phi Delta)-probabilistic contractor couple selective operator nonlinear operator equations
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INVARIANTS-PRESERVING DU FORT-FRANKEL SCHEMES AND THEIR ANALYSES FOR NONLINEAR SCHRÖDINGER EQUATIONS WITH WAVE OPERATOR
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作者 Dingwen Deng Zhijun Li 《Journal of Computational Mathematics》 SCIE CSCD 2024年第3期814-850,共37页
Du Fort-Frankel finite difference method(FDM)was firstly proposed for linear diffusion equations with periodic boundary conditions by Du Fort and Frankel in 1953.It is an explicit and unconditionally von Neumann stabl... Du Fort-Frankel finite difference method(FDM)was firstly proposed for linear diffusion equations with periodic boundary conditions by Du Fort and Frankel in 1953.It is an explicit and unconditionally von Neumann stable scheme.However,there has been no research work on numerical solutions of nonlinear Schrödinger equations with wave operator by using Du Fort-Frankel-type finite difference methods(FDMs).In this study,a class of invariants-preserving Du Fort-Frankel-type FDMs are firstly proposed for one-dimensional(1D)and two-dimensional(2D)nonlinear Schrödinger equations with wave operator.By using the discrete energy method,it is shown that their solutions possess the discrete energy and mass conservative laws,and conditionally converge to exact solutions with an order of for ofο(T^(2)+h_(x)^(2)+(T/h_(x))^(2))1D problem and an order ofο(T^(2)+h_(x)^(2)+h_(Y)^(2)+(T/h_(X))^(2)+(T/h_(y))^(2))for 2D problem in H1-norm.Here,τdenotes time-step size,while,hx and hy represent spatial meshsizes in x-and y-directions,respectively.Then,by introducing a stabilized term,a type of stabilized invariants-preserving Du Fort-Frankel-type FDMs are devised.They not only preserve the discrete energies and masses,but also own much better stability than original schemes.Finally,numerical results demonstrate the theoretical analyses. 展开更多
关键词 nonlinear Schrodinger equations with wave operator Du Fort-Frankel finite difference methods Discrete energy and mass conservative laws Numerical convergence
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A Posteriori Parameter Choice Strategy for Nonlinear Monotone Operator Equations
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作者 Hong-qi Yang, Zong-yi HouDepartment of Scientific Computing & Computer Applications, Zhongshan University, Guangzhou 510275,ChinaDepartment of Mathematics, Pudan University, Shanghai 200433, China 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2002年第2期289-294,共6页
In this paper we present an a posteriori parameter choice strategy for nonlinear ill-posed operator equations involving monotone operators. Under certain conditions, this a posteriori parameter choice strategy guarant... In this paper we present an a posteriori parameter choice strategy for nonlinear ill-posed operator equations involving monotone operators. Under certain conditions, this a posteriori parameter choice strategy guarantees the optimal convergence rate O (δ1/2) for Tikhonov-Browder regularization, where δ denotes the noise level of the data perturbation. 展开更多
关键词 nonlinear operator equation monotone operator convergence rate a posteriori parameter choice
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Lipschitz Operators and the Solvability of Non-linear Operator Equations 被引量:2
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作者 HuaiXinCAO ZongBenXU 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2004年第3期499-506,共8页
Let U and V be Banach spaces, L and N be non-linear operators from U into V. L is said to be Lipschitz if L 1(L) := sup{∥Lx - Ly∥ · ∥x - y∥-1 : x ≠ y} is finite. In this paper, we give some basic properties ... Let U and V be Banach spaces, L and N be non-linear operators from U into V. L is said to be Lipschitz if L 1(L) := sup{∥Lx - Ly∥ · ∥x - y∥-1 : x ≠ y} is finite. In this paper, we give some basic properties of Lipschitz operators and then discuss the unique solvability, exact solvability, approximate solvability of the operator equations Lx = y and Lx + Nx = y. Under some conditions we prove the equivalence of these solvabilities. We also give an estimation for the relative-errors of the solutions of these two systems and an application of our method to a non-linear control system. 展开更多
关键词 Lipschitz operator nonlinear operator equation SOLVABILITY Control system CONTROLLABILITY
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A Newton type iterative method for heat-conduction inverse problems
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作者 贺国强 孟泽红 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2007年第4期531-539,共9页
An inverse problem for identification of the coefficient in heat-conduction equation is considered. After reducing the problem to a nonlinear ill-posed operator equation, Newton type iterative methods are considered. ... An inverse problem for identification of the coefficient in heat-conduction equation is considered. After reducing the problem to a nonlinear ill-posed operator equation, Newton type iterative methods are considered. The implicit iterative method is applied to the linearized Newton equation, and the key step in the process is that a new reasonable a posteriori stopping rule for the inner iteration is presented. Numerical experiments for the new method as well as for Tikhonov method and Bakushikskii method are given, and these results show the obvious advantages of the new method over the other ones. 展开更多
关键词 inverse problems nonlinear ill-posed operator equations Newton type method implicit iterative method iteration stopping rule
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Convergence of Newton's Method and Uniqueness of the Solution of Equations in Banach SpacesⅡ 被引量:15
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作者 XingHuaWANG ChongLI 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2003年第2期405-412,共8页
Some results on convergence of Newton's method in Banach spaces are established under the assumption that the derivative of the operators satisfies the radius or center Lipschitz condition with a weak L average.
关键词 nonlinear operator equation Newton's method Lipschitz condition with L average Convergence ball
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Study on a General Hopf Hierarchy
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作者 崔敏婕 楼森岳 《Communications in Theoretical Physics》 SCIE CAS CSCD 2016年第4期393-396,共4页
By using a general symmetry theory related to invariant functions,strong symmetry operators and hereditary operators,we find a general integrable hopf heirarchy with infinitely many general symmetries and Lax pairs.Fo... By using a general symmetry theory related to invariant functions,strong symmetry operators and hereditary operators,we find a general integrable hopf heirarchy with infinitely many general symmetries and Lax pairs.For the first order Hopf equation,there exist infinitely many symmetries which can be expressed by means of an arbitrary function in arbitrary dimensions.The general solution of the first order Hopf equation is obtained via hodograph transformation.For the second order Hopf equation,the Hopf-diffusion equation,there are five sets of infinitely many symmetries.Especially,there exist a set of primary branch symmetry with which contains an arbitrary solution of the usual linear diffusion equation.Some special implicit exact group invariant solutions of the Hopf-diffusion equation are also given. 展开更多
关键词 Hopf hierarchy symmetries hereditary operator exact solutions nonlinear diffusion equations
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