In this study, we will construct numerical techniques for tackling the logarithmic Schrödinger’s nonlinear equation utilizing the explicit scheme and the Crank-Nicolson scheme of the finite difference method...In this study, we will construct numerical techniques for tackling the logarithmic Schrödinger’s nonlinear equation utilizing the explicit scheme and the Crank-Nicolson scheme of the finite difference method. These schemes will be subjected to accuracy and stability tests before being used. Efficacy and robustness of the techniques under consideration will be demonstrated using an exact solution, one-Gausson, as well as conserved quantities. Interaction of two-soliton will be conducted. The numerical findings revealed, the interplay behavior is flexible.展开更多
Explicit bounds on bounded solutions to a new class of Volterra-type linear and nonlinear discrete inequalities involving infinite sums are established. These inequalities can be viewed as discrete analogues of some V...Explicit bounds on bounded solutions to a new class of Volterra-type linear and nonlinear discrete inequalities involving infinite sums are established. These inequalities can be viewed as discrete analogues of some Volterra-type inequalities having improper integral functionals,which are new to the literature.展开更多
Recently, many authors have studied the following CH-γequation: ut + c0ux + 3uux -α2(wxxt + uuxxx + 2uxuxx) 4-γuxxx = 0,whereα2, c0 andγare paramters. Its bounded wave solutions have been investigated mainly for ...Recently, many authors have studied the following CH-γequation: ut + c0ux + 3uux -α2(wxxt + uuxxx + 2uxuxx) 4-γuxxx = 0,whereα2, c0 andγare paramters. Its bounded wave solutions have been investigated mainly for the caseα2 > 0. For the caseα2 < 0, the existence of three bounded waves (regular solitary waves, compactons, periodic peakons) was pointed out by Dullin et al. But the proof has not been given. In this paper, not only the existence of four types of bounded waves: periodic waves, compacton-like waves, kink-like waves, regular solitary waves, is shown, but also their explicit expressions or implicit expressions are given for the caseα2 < 0. Some planar graphs of the bounded wave solutions and their numerical simulations are given to show the correctness of our results.展开更多
We consider the problem of discriminating general quantum operations. Using the definition of mapping operator to vector, and by some calculating skills, we derive an explicit formulation as a new bound on the minimum...We consider the problem of discriminating general quantum operations. Using the definition of mapping operator to vector, and by some calculating skills, we derive an explicit formulation as a new bound on the minimum-error probability for ambiguous discrimination between arbitrary m quantum operations. This formulation consists only of Kraus-operators, the dimension, and the priori probabilities of the discriminated quantum operations, and is independent of input states. To some extent, we further generalize the bounds on the minimum-error probability for discriminating mixed states to quantum operations.展开更多
文摘In this study, we will construct numerical techniques for tackling the logarithmic Schrödinger’s nonlinear equation utilizing the explicit scheme and the Crank-Nicolson scheme of the finite difference method. These schemes will be subjected to accuracy and stability tests before being used. Efficacy and robustness of the techniques under consideration will be demonstrated using an exact solution, one-Gausson, as well as conserved quantities. Interaction of two-soliton will be conducted. The numerical findings revealed, the interplay behavior is flexible.
文摘Explicit bounds on bounded solutions to a new class of Volterra-type linear and nonlinear discrete inequalities involving infinite sums are established. These inequalities can be viewed as discrete analogues of some Volterra-type inequalities having improper integral functionals,which are new to the literature.
基金This work was supported by the National Natural Science Foundation of China (Grant No. 10571062)
文摘Recently, many authors have studied the following CH-γequation: ut + c0ux + 3uux -α2(wxxt + uuxxx + 2uxuxx) 4-γuxxx = 0,whereα2, c0 andγare paramters. Its bounded wave solutions have been investigated mainly for the caseα2 > 0. For the caseα2 < 0, the existence of three bounded waves (regular solitary waves, compactons, periodic peakons) was pointed out by Dullin et al. But the proof has not been given. In this paper, not only the existence of four types of bounded waves: periodic waves, compacton-like waves, kink-like waves, regular solitary waves, is shown, but also their explicit expressions or implicit expressions are given for the caseα2 < 0. Some planar graphs of the bounded wave solutions and their numerical simulations are given to show the correctness of our results.
基金Supported by the Special Funds of the National Natural Science Foundation of China under Grant No.11247310the Foundation for Distinguished Young Talents in Higher Education of Guangdong under Grant No.2012LYM 0096the Start-up Funding of Hanshan Normal University under Grant No.QD20111123
文摘We consider the problem of discriminating general quantum operations. Using the definition of mapping operator to vector, and by some calculating skills, we derive an explicit formulation as a new bound on the minimum-error probability for ambiguous discrimination between arbitrary m quantum operations. This formulation consists only of Kraus-operators, the dimension, and the priori probabilities of the discriminated quantum operations, and is independent of input states. To some extent, we further generalize the bounds on the minimum-error probability for discriminating mixed states to quantum operations.
