THE SOLITARY WAVE MODEL OF SUPERFLUIDITY

2005 ◽  
Vol 19 (01n03) ◽  
pp. 99-102 ◽  
Author(s):  
KUANGDING PENG
Keyword(s):  
Exact Solution ◽  
Transition Temperature ◽  
Solitary Wave ◽  
Schrödinger Equation ◽  
Harmonic Oscillator ◽  
Solitary Waves ◽  
Schrodinger Equation ◽  
Wave Model ◽  
Harmonic Oscillator Model ◽  
Coherent Condition

We propose the solitary wave model of superfluidity. According to harmonic oscillator model of quasi-lattice of liquid, it is proven that superfluid domains (SD) exist in He liquid, in which the resistanceless motion of liquid molecules (LM) can be carry out. At temperature lower than T c, all SD connect with each other and superflow in whole liquid takes place. Applying Toda's potential, under continuous conditions, we obtain the motion equation of LM, and its exact solution. Substituting these results into Schrödinger equation of LM, we can prove the existence of solitary waves of LM and the non-linear Schrödinger equation of LM. The motion of solitons of LM leads to a superflow. On the basis of coherent condition of wave of LM, we derive the formula of transition temperature Tc of superfluidity. From the formula, the relation of the onset temperature Tc of superflow on inert layers is explained.

scholarly journals COMPLEXIFIER VERSUS FACTORIZATION AND DEFORMATION METHODS FOR GENERATION OF COHERENT STATES OF A 1D NLHO I: MATHEMATICAL CONSTRUCTION

2013 ◽  
Vol 10 (10) ◽  
pp. 1350056 ◽  
Author(s):  
R. ROKNIZADEH ◽  
H. HEYDARI
Keyword(s):  
Exact Solution ◽  
Schrödinger Equation ◽  
Harmonic Oscillator ◽  
Coherent States ◽  
Schrodinger Equation ◽  
Jacobi Polynomials ◽  
One Dimensional ◽  
The Difference ◽  
Mathematical Construction

Three methods: complexifier, factorization and deformation, for construction of coherent states are presented for one-dimensional nonlinear harmonic oscillator (1D NLHO). Since by exploring the Jacobi polynomials [Formula: see text], bridging the difference between them is possible, we give here also the exact solution of Schrödinger equation of 1D NLHO in terms of Jacobi polynomials.

scholarly journals Schrödinger equation of a particle in a uniformly accelerated frame and the possibility of a new kind of quanta

2015 ◽  
Vol 30 (38) ◽  
pp. 1550182 ◽  
Author(s):  
Sanchari De ◽  
Sutapa Ghosh ◽  
Somenath Chakrabarty
Keyword(s):  
Exact Solution ◽  
Hydrogen Atom ◽  
Schrödinger Equation ◽  
Harmonic Oscillator ◽  
Schrodinger Equation ◽  
Energy Levels ◽  
Minkowski Spacetime ◽  
Quantum Harmonic Oscillator ◽  
One Dimensional ◽  
Spacetime Geometry

In this paper, we have developed a formalism to obtain the Schrödinger equation for a particle in a frame undergoing a uniform acceleration in an otherwise flat Minkowski spacetime geometry. We have presented an exact solution of the equation and obtained the eigenfunctions and the corresponding eigenvalues. It has been observed that the Schrödinger equation can be reduced to a one-dimensional hydrogen atom problem. Whereas, the quantized energy levels are exactly identical with that of a one-dimensional quantum harmonic oscillator. Hence, considering transitions, we have predicted the existence of a new kind of quanta, which will either be emitted or absorbed if the particles get excited or de-excited, respectively.

OPTICAL SOLITARY WAVES FOR THE GENERALIZED HIGHER-ORDER NONLINEAR SCHRÖDINGER EQUATION WITH VARIABLE COEFFICIENTS

2007 ◽  
Vol 21 (17) ◽  
pp. 2951-2964 ◽  
Author(s):  
CHAO-QING DAI ◽  
GUO-QUAN ZHOU ◽  
JIE-FANG ZHANG
Keyword(s):  
Solitary Wave ◽  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Solitary Waves ◽  
Schrodinger Equation ◽  
Variable Coefficients ◽  
Higher Order ◽  
Nonlinear Schrodinger Equation ◽  
Solitary Wave Solutions ◽  
Wave Solutions

In this paper, four kinds of optical solitary wave solutions, including bright, dark optical solitary waves and new types of solitary waves (W-shaped and M-shaped), for the generalized higher-order nonlinear Schrödinger equation (GHONLSE) with variable coefficients are considered under certain parametric conditions. Among these solutions, the W-shaped and M-shaped solitary waves, which cannot exist in the variable-coefficient nonlinear Schrödinger equation (vNLSE), are first given for the GHONLSE with variable coefficients. As examples, we analyze the properties of these solitary wave solutions in some periodic distributed amplification systems. When α1(z)=0, these bright and dark optical solitary wave solutions agree with the corresponding solutions in Refs. 25, 26 and 27, and the W-shaped solitary wave is in agreement with the corresponding result in Ref. 29. When α3(z)–α7(z) are constants and α1(z)=α2(z)=0, the W-shaped and M-shaped solitary waves in Refs. 14 and 15 can be recovered, respectively. Under the absence of the higher-order terms (α4(z), α6(z), α7(z)) and α1(z)=0, we provide the same results as reported in Refs. 22 and 23. This means that our results have more general forms than the earlier reports.

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