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Dynamics of cubic and quintic nonlinear Schr dinger equations
立方五次方非线性Schr dinger方程的动力学性质研究

Hua Wei,Liu Xue-Shen,

物理学报 , 2011,
Abstract: We solve one-dimensional(1D) cubic and quintic nonlinear Schr dinger equations by the symplectic method. The dynamical property of the nonlinear Schr dinger equation is studied with using diffenent nonlinear coefficients. The results show that the system presents quasiperiodic solution, chaotic solution, and periodic solution with the cubic nonlinear coefficient increasing, and the breather solution reduced into a fundamental soliton solution under the modulation of the quintic nonlinear coefficient.
Wavelet basis for the Schr?dinger equation  [PDF]
M. V. Altaiski
Physics , 1995,
Abstract: The self-similar representation for the Schr\"{o}dinger equation is derived.
Asymptotic solutions of perturbed N-component nonlinear Schr?dinger equations

Cheng Xue-Ping,Lin Ji,Wang Zhi-Ping,

物理学报 , 2007,
Abstract: 将直接微扰方法应用于可积的含修正项的非线性薛定谔方程,通过近似解与精确解的比较确定了直接微扰方法的可靠性.继而,将该方法应用于微扰的耦合非线性薛定谔方程,并获得了该微扰方程的可靠的近似解.
On the linearity of the Schr?dinger equation
Bialynicki-Birula, Iwo;
Brazilian Journal of Physics , 2005, DOI: 10.1590/S0103-97332005000200003
Abstract: the problem of the linearity of the schr?dinger equation is described from a historical perspective. it is argued that the schr?dinger picture on which this equation is based cannot be retained in relativistic quantum theory. a closer analysis of realistic experiments might offer a clue how to modify the evolution equation for the state vectors in quantum field theory.
Finite Temperature Schr?dinger Equation  [PDF]
Xiang-Yao Wu,Bai-Jun Zhang,Xiao-Jing Liu,Nuo Ba,Yi-Heng Wu,Qing-Cai Wang,Yan Wang
Physics , 2010, DOI: 10.1007/s10773-011-0745-7
Abstract: We know Schr\"{o}dinger equation describes the dynamics of quantum systems, which don't include temperature. In this paper, we propose finite temperature Schr\"{o}dinger equation, which can describe the quantum systems in an arbitrary temperature. When the temperature T=0, it become Shr\"{o}dinger equation.
Global Schr?dinger maps  [PDF]
Ioan Bejenaru,Alexandru D. Ionescu,Carlos E. Kenig,Daniel Tataru
Mathematics , 2008,
Abstract: We consider the Schr\"{o}dinger map initial-value problem in dimension two or greater. We prove that the Schr\"{o}dinger map initial-value problem admits a unique global smooth solution, provided that the initial data is smooth and small in the critical Sobolev space. We prove also that the solution operator extends continuously to the critical Sobolev space.
On the Schr?dinger group  [PDF]
Guy Roger Biyogmam
Mathematics , 2013,
Abstract: In this paper, we compute the Leibniz homology of the Schr\"{o}dinger algebra. We show that it is a graded vector space generated by tensors in dimensions $2n-2$ and $2n$. The Leibniz homology of the full Galilei algebra is also calculated.
Derivation of Nonlinear Schr?dinger Equation  [PDF]
Xiang-Yao Wu,Bai-Jun Zhang,Xiao-Jing Liu,Li-Xiao,Yi-Heng Wu,Yan-Wang,Qing-Cai Wang,Shuang Cheng
Physics , 2011,
Abstract: We propose some nonlinear Schr\"{o}dinger equations by adding some higher order terms to the Lagrangian density of Schr\"{o}dinger field, and obtain the Gross-Pitaevskii (GP) equation and the logarithmic form equation naturally. In addition, we prove the coefficient of nonlinear term is very small, i.e., the nonlinearity of Schr\"{o}dinger equation is weak.
Symmetrized Schr?dinger Equation and General Complex Solution  [PDF]
Yihuan Wei
Physics , 2003,
Abstract: We suggest the symmetrized Schr\"{o}dinger equation and propose a general complex solution which is characterized by the imaginary units $i$ and $\epsilon$. This symmetrized Schr\"{o}dinger equation appears some interesting features.
Quantization Rules for Bound States of the Schr?dinger Equation  [PDF]
Zhong-Qi Ma,Bo-Wei Xu
Physics , 2004, DOI: 10.1142/S0218301305003429
Abstract: An exact quantization rule for the bound states of the one-dimensional Schr\"{o}dinger equation is presented and is generalized to the three-dimensional Schr\"{o}dinger equation with a spherically symmetric potential.
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