A high order energy preserving scheme for the strongly coupled nonlinear Schrōdinger system

A high order energy preserving scheme for a strongly coupled nonlinear Schrōdinger system is roposed by using the average vector field method. The high order energy preserving scheme is applied to simulate the soliton evolution of the strongly coupled Schrōdinger system. Numerical results show that the high order energy preserving scheme can well simulate the soliton evolution, moreover, it preserves the discrete energy of the strongly coupled nonlinear Schrōdinger system exactly.     

Effect of structural parameters of Gaussian repaired pit on light intensity distribution inside KH_2PO_4 crystal

KH2PO4 （KDP） crystal with excellent optical properties is a very important element of inertial confinement fusion （ICF） device. However, KDP crystal surface micro-defects severely reduce the crystal laser damage threshold, affecting the crystal service life. In this paper, Gaussian repaired pit is used to replace the crystal surface micro-defects, in order to improve the laser damage resistance of the KDP crystal with surface micro-defects. At first, the physical model of Gaussian repaired pit is built by Fourier model method, and the accuracy of the method is analyzed. It is found that the calculation error can be reduced by increasing the product of the width-period ratio and the truncation constant of the repaired pit. The calculation results about the physical model of Gaussian repaired pit show that the light intensity distribution within the crystal is symmetrical, and there are evidently enhanced light intensity regions in the crystal. Meanwhile, the maximum relative intensity inside the KDP crystal decreases gradually with the increase of the width of the Gaussian repaired pit. Secondly, the Gaussian repaired pits with different widths and the same depth of 20 μm are processed by micro-milling. Their surfaces are very smooth and present the ductile cutting state under the microscope. Finally, the laser damage threshold of the Gaussian repaired pits on the surface of the KDP crystal sample is measured by a 3 ω, 6-ns laser. The results showthat the maximum threshold of the Gaussian repaired pits is 3.12 J/cm2, which is 60% higher than the threshold of initial damage point, and the laser damage threshold increases with the increase of the width of the Gaussian repaired pit.     

Effects of the vibrational and rotational excitation of reagent on the stereodynamics of the reaction S（3P） + H2→ SH + H

Quasiclassical trajectory （QCT） calculations are first carried out to study the stereodynamics of the S （3p） ＋ H2 → SH ＋ H reaction based on the ab initio 13Atr potential energy surface （PES） （Lii etal. 2012 J. Chem. Phys. 136 094308）. The QCT-calculated reaction probabilities and cross sections for the S ＋ H2 （v = 0, j = 0） reaction are in good agreement with the previous quantum mechanics （QM） results. The vector properties including the alignment, orientation, and polarization- dependent differential cross sections （PDDCSs） of the product SH are presented at a collision energy of 1.8 eV. The effects of the vibrational and rotational excitations of reagent on the stereodynamics are also investigated and discussed in the present work. The calculated QCT results indicate that the vibrational and rotational excitations of reagent play an important role in determining the stereodynamic properties of the title reaction.     

A new magneto-cardiogram study using a vector model with a virtual heart and the boundary element method

A cardiac vector model is presented and verified, and then the forward problem for cardiac magnetic fields and electric potential are discussed based on this model and the realistic human torso volume conductor model, including lungs. A torso-cardiac vector model is used for a 12-lead electrocardiographic (ECG) and magneto-cardiogram (MCG) simulation study by using the boundary element method (BEM). Also, we obtain the MCG wave picture using a compound four-channel HTc ·SQUID system in a magnetically shielded room. By comparing the simulated results and experimental results, we verify the cardiac vector model and then do a preliminary study of the forward problem of MCG and ECG. Therefore, the results show that the vector model is reasonable in cardiac electrophysiology.     

Stereodynamics of the O（^3p） with H： （D2） （v = O,j =O） reaction

Quasi-classical trajectory theory is used to study the reaction of O（3p） with H2 （D2） based on the ground 3A″ potential energy surface （PES）. The reaction cross section of the reaction O＋H2→＋OH＋H is in excellent agreement with the previous result. Vector correlations, product rotational alignment parameters （P2（j′. k）） and several polarizeddependent differential cross sections are further calculated for the reaction. The product polarization distribution exhibits different characteristics that can be ascribed to different motion paths on the PES, arising from various collision energies or mass factors.     

Effective Action for Noncommutative U（1） Gauge Theory with Higher Dimensional Terms

In this paper we apply the assumption of our recent work in noncommutative scalar models to the noncommutative U（1） gauge theories. This assumption is that the noneommutative effects start to be visible continuously from a scale ANC and that below this scale the theory is a commutative one. Based on this assumption and using background field method and loop calculations, an effective action is derived for noncommutative U（1） gauge theory. It will be shown that the corresponding low energy effective theory is asymptotically free and that under this condition the noncommutative quadratic IR divergences will not appear. The effective theory contains higher dimensional terms, which become more important at high energies. These terms predict an elastic photon-photon scattering due to the noncommutativity of space. The coefficients of these higher dimensional terms also satisfy a positivity constraint indicating that in this theory the related diseases of superluminal signal propagating and bad analytic properties of S-matrix do not exist. In the last section, we will apply our method to the noncommutative extra dimension theories.     

Exact Solutions to a Combined sinh-cosh-Gordon Equation

Based on a transformed Painlev~ property and the variable separated ODE method, a function transfor- mation method is proposed to search for exact solutions of some partial differential equations （PDEs） with hyperbolic or exponential functions. This approach provides a more systematical and convenient handling of the solution process of this kind of nonlinear equations. Its key point is to eradicate the hyperbolic or exponential terms by a transformed Painleve property and reduce the given PDEs to a variable-coefficient the resulting equations by some methods. As an application, are formally derived. ordinary differential equations, then we seek for solutions to exact solutions for the combined sinh-cosh-Gordon equation     

Various Methods for Constructing Auto-Baicklund Transformations for a Generalized Variable-Coefficient Korteweg-de Vries Model from Plasmas and Fluid Dynamics

In this paper, under the Painleve-integrable condition, the auto-Biicklund transformations in different forms for a variable-coefficient Korteweg-de Vries model with physical interests are obtained through various methods including the Hirota method, truncated Painleve expansion method, extendedvariable-coefficient balancing-act method, and Lax pair. Additionally, the compatibility for the truncated Painleve expansion method and extended variable-coetfficient balancing-act method is testified.     

Approximate Similarity Reduction for Perturbed Kaup-Kupershmidt Equation via Lie Symmetry Method and Direct Method

The perturbed Kaup-Kupershmidt equation is investigated in terms of the approximate symmetry perturbation method and the approximate direct method. The similarity reduction solutions of different orders are obtained for both methods, series reduction solutions are consequently derived. Higher order similarity reduction equations are linear variable coefficients ordinary differential equations. By comparison, it is find that the results generated from the approximate direct method are more general than the results generated from the approximate symmetry perturbation method.     

（G′/G）-Expansion Method Equivalent to Extended Tanh Function Method

In a recent article [Physics Letters A 372 （2008） 417], Wang et al. proposed a method, which is called the （G′/G）-expansion method, to look for travelling wave solutions of nonlinear evolution equations. The travelling wave solutions involving parameters of the KdV equation, the mKdV equation, the variant Boussinesq equations, and the Hirota-Satsuma equations are obtained by using this method. They think the （G′/G）-expansion method is a new method and more travelling wave solutions of many nonlinear evolution equations can be obtained. In this paper, we will show that the （G′/G）-expansion method is equivalent to the extended tanh function method.     

Analytical and Numerical Studies of Quantum Plateau State in One Alternating Heisenberg Chain

By using the coupled duster method and the numerical density matrix renormalization group method, we investigate the properties of the quantum plateau state in an alternating Heisenberg spin chain. In the absence of a magnetic field, the results obtained from the coupled cluster method and density matrix renormalization group method both show that the ground state of the aiternating chain is a gapped dimerized state when the parameter a exceeds a critical point ac. The value of the critical points can be determined precisely by a detailed investigation of the behavior of the spin gap. The system therefore possesses an m = 0 plateau state in the presence of a magnetic field When a 〉 ac. In addition to the m = 0 plateau state, the results of density matrix renormaiization group indicate that there is an m = 1/4 plateau state that occurs between two critical fields in the alternating chain if a 〉 1. The mechanism for the m = 1/4 plateau state and the critical behavior of the magnetization as one approaches this plateau state are also discussed.     

An element-free Galerkin （EFG） method for numerical solution of the coupled Schrodinger-KdV equations

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.     

Symbolic Computations and Exact and Explicit Solutions of Some Nonlinear Evolution Equations in Mathematical Physics

With the aid of symbolic computation system Mathematica, several explicit solutions for Fisher＇s equation and CKdV equation are constructed by utilizing an auxiliary equation method, the so called G′/G-expansion method, where the new and more general forms of solutions are also constructed. When the parameters are taken as special values, the previously known solutions are recovered.     

A connection between the （G′/G）-expansion method and the truncated Painlev ＇e expansion method and its application to the mKdV equation

Recently the （G′/G）-expansion method was proposed to find the traveling wave solutions of nonlinear evolution equations. This paper shows that the （G′/G）-expansion method is a special form of the truncated Painlev＇e expansion method by introducing an intermediate expansion method. Then the generalized （G′/G）-（G/G′） expansion method is naturally derived from the standpoint of the nonstandard truncated Painlev＇e expansion. The application of the generalized method to the mKdV equation shows that it extends the range of exact solutions obtained by using the （ G′/ G）-expansion method.     

Exact Solutions to （2＋1）-Dimensional Kaup-Kupershmidt Equation

In this paper, by using the symmetry method, the relationships between new explicit solutions and old ones of the （2＋1）-dimensional Kaup-Kupershmidt （KK） equation are presented. We successfully obtain more general exact travelling wave solutions for （2＋ 1）-dimensional KK equation by the symmetry method and the （G1/G）-expansion method. Consequently, we find some new solutions of （2＋1）-dimensional KK equation, including similarity solutions, solitary wave solutions, and periodic solutions.     

Elastic Scattering of CH4 by Electron Impact

In this work we present a theoretical study on electrons scattering by CH4 in the intermediate energy range. More specifically, we report integral and differential cross sections for electron scattering by CH4 in the （10 - 300） eV range by the Schwinger multichannel method using plane waves as a trial basis set （SMC-PW）. To include exchange effects we have used the Born-Ochkur model. Our aim is to study the numerical stability of the cross sections and our calculated results compared with experimental data and theoretical studies are encouraging.     

Passive polarization rotator based on silica photonic crystal fiber for 1.31-μm and 1.55-μm bands via adjusting the fiber length

A new polarization rotator based on the silica photonic crystal fiber is proposed. The proposed polarization rotator photonic crystal fiber （PR-PCF） possesses a triangle jigsaw-shape core region. The full-vector finite-element method is used to analyze the phenomenon of polarization conversion between the quasi-TE and quasi-TM modes. Numerical simulations show that the wavelengths of 1.31 μm and 1.55 μm are converted with a nearly 100% polarization conversion ratio with their matched coupling length and has a relatively strong realistic fabrication tolerance - 100 nm on the y axis and 50 nm on the x axis. The full vectorial finite difference beam propagation method is used to confirm the performance of the proposed PR-PCF.     

Bilinear Backlund transformation and explicit solutions for a nonlinear evolution equation

The bilinear form of two nonlinear evolution equations are derived by using Hirota derivative. The Backlund transformation based on the Hirota bilinear method for these two equations are presented, respectively. As an application, the explicit solutions including soliton and stationary rational solutions for these two equations are obtained.     

A conservative Fourier pseudospectral algorithm for the nonlinear Schrdinger equation

In this paper, we derive a new method for a nonlinear Schrodinger system by using the square of the first-order Fourier spectral differentiation matrix D1 instead of the traditional second-order Fourier spectral differentiation matrix D2 to approximate the second derivative. We prove that the proposed method preserves the charge and energy conservation laws exactly. A deduction argument is used to prove that the numerical solution is second-order convergent to the exact solutions in ｜｜·｜｜2 norm. Some numerical results are reported to illustrate the efficiency of the new scheme in preserving the charge and energy conservation laws.     

Solitons for a generalized variable-coefficient nonlinear SchrSdinger equation

In this paper, we investigate some exact soliton solutions for a generalized variable-coefficients nonlinear SchrSdinger equation （NLS） with an arbitrary time-dependent linear potential which describes the dynamics of soliton solutions in quasi-one-dimensional Bose-Einstein condensations. Under some reasonable assumptions, one-soliton and two-soliton solutions are constructed analytically by the Hirota method. From our results, some previous one- and two- soliton solutions for some NLS-type equations can be recovered by some appropriate selection of the various parameters. Some figures are given to demonstrate some properties of the one- and the two-soliton and the discussion about the integrability property and the Hirota method is given finally.