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81.
在半离散格式下研究一类带幂次非线性项的Schr(o)dinger方程的非协调矩形EQrot1元方法.直接利用插值技巧和该单元的两个特殊性质(相容误差比插值误差高一阶及其插值算子与传统的Ritz投影是一致的),给出相应的收敛性分析及误差估计. 相似文献
82.
An element-free Galerkin (EFG) method for numerical solution of the coupled Schrodinger-KdV equations
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The present paper deals with the numerical solution of the coupled Schrodinger-KdV equations using the elementfree Galerkin (EFG) method which is based on the moving least-square approximation. Instead of traditional mesh oriented methods such as the finite difference method (FDM) and the finite element method (FEM), this method needs only scattered nodes in the domain. For this scheme, a variational method is used to obtain discrete equations and the essential boundary conditions are enforced by the penalty method. In numerical experiments, the results are presented and compared with the findings of the finite element method, the radial basis functions method, and an analytical solution to confirm the good accuracy of the presented scheme. 相似文献
83.
By using the theory of cavity QED, we study the system in which a two-level atom interacts with a cavity in the case of large detuning. Through the selective detecting of atomic state, Schrodinger cat states and entangled coherent states are easily generated. When the atom is driven by a weak classical field and the cavity field is in the Schrodinger cat state, we study the conditions of generating the Fock states and the maximal success probability. The maximal success probability in our scheme is larger than the previous one. 相似文献
84.
Temporal evolution of wavepacket tunneling in a periodic double-well torsional potential has been studied numerically. Peculiarities
of wavepacket tunneling dynamics under conditions of asymmetric distortion of the periodic potential function have been analyzed.
__________
Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 75, No. 3, pp. 342–346, May–June, 2008. 相似文献
85.
Shuji Watanabe 《Proceedings of the American Mathematical Society》1997,125(1):129-136
Spaces of Sobolev type are discussed, which are defined by the operator with singularity: , where and . This operator appears in a one-dimensional harmonic oscillator governed by Wigner's commutation relations. Smoothness of and continuity of () are studied where is in each space of Sobolev type, and results similar to Sobolev's lemma are obtained. The proofs are carried out based on a generalization of the Fourier transform. The results are applied to the Schrödinger equation.
86.
Janusz Walorski 《Proceedings of the American Mathematical Society》1997,125(1):153-158
The problem of the existence and uniqueness of increasing and convex solutions of the Schröder equation, defined on cones in Banach spaces, is examined on a base of the Krein-Rutman theorem.
87.
Daniella Bekiranov Takayoshi Ogawa Gustavo Ponce 《Proceedings of the American Mathematical Society》1997,125(10):2907-2919
An interaction equation of the capillary-gravity wave is considered. We show that the Cauchy problem of the coupled Schrödinger-KdV equation,
is locally well-posed for weak initial data . We apply the analogous method for estimating the nonlinear coupling terms developed by Bourgain and refined by Kenig, Ponce, and Vega.
88.
E. Grenier 《Proceedings of the American Mathematical Society》1998,126(2):523-530
We study the semi-classical limit of the nonlinear Schrödinger equation for initial data with Sobolev regularity, before shocks appear in the limit system, and in particular the validity of the WKB method.
89.
In this paper, we obtain the necessary and sufficient conditions for having the maximum principle and existence of positive solutions for some cooperative systems involving Schrödinger operators defined on unbounded domains. Then, we deduce the existence of solutions for semi-linear systems. Finally we discuss the generalized maximum principle (gf q -positivity) for non cooperative systems. 相似文献
90.
We use the method of point canonical transformations and choose the Rosen-Morse-type potential as the reference potential
to study exact solutions of the position-dependent effective mass Schr?dinger equations. Choosing three position-dependent
mass distributions, we construct seven exactly solvable target potentials with PT symmetry. The energy spectra of the bound
states and corresponding wavefunctions for the PT-symmetric potentials are given in the exact closed forms. We also discuss
the isospectrality of different Schr?dinger equations with the same mass distribution or different mass distributions for
different PT-symmetric potentials.
相似文献