Solitary wave interaction in a compact equation for deep-water gravity waves

We compute numerical traveling wave solutions to a compact version of the Zakharov equation for unidirectional deep-water waves recently derived by Dyachenko and Zakharov [1]. Furthermore, by means of an accurate Fourier-type spectral scheme we find that solitary waves appear to collide elastically, suggesting the integrability of the Zakharov equation.     

Effect of adiabatic variation of dust charges on dust acoustic solitary waves in magnetized dusty plasmas

The effect of dust charging and the influence of its adiabatic variation on dust acoustic waves is investigated. By employing the reductive perturbation technique we derived a Zakharov－Kuznetsov (ZK) equation for small amplitude dust acoustic waves. We have analytically verified that there are only rarefactive solitary waves for this system. The instability region for one-dimensional solitary wave under transverse perturbations has also been obtained. The obliquely propagating solitary waves to the z-direction for the ZK equation are given in this paper as well.     

A Pair of Zakharov Equations with Collisional Damping and the Motion of Langmuir Soliton

The effects of collisional damping on high frequency Langmuir wave and low frequency ion-acoustic wave have been investigated. It is found that the governing equations for the waves are a pair of Zakharov equations with a damping term in each equation. By using the treatment which consists of approximate solutions of the balance equations, a set of first order ordinary differential equations have been derived for the solution parameters in order to study the motion of Zakharov solitons in presence of damping. It has been shown that the width of the soliton remains constant throughout the motion.     

On the persistence of breathers at deep water

The long-time behavior of a perturbation to a uniform wavetrain of the compact Zakharov equation is studied near the modulational instability threshold. A multiple-scale analysis reveals that the perturbation evolves in accord with a focusing nonlinear Schrodinger equation for values of wave steepness μ < μ₁ ≈ 0.274. The long-time dynamics is characterized by interacting breathers, homoclinic orbits to an unstable wavetrain. The associated Benjamin-Feir index is a decreasing function of μ, and it vanishes at μ₁. Above this threshold, the perturbation dynamics is of defocusing type and breathers are suppressed. Thus, homoclinic orbits persist only for small values of wave steepness μ ? μ₁, in agreement with recent experimental and numerical observations of breathers.     

铷原子中参量六波混频和量子拍的研究

在铷原子中实现了轴向相位匹配的参量六波混频,并探测到位于红外光谱区的六波混频信号.六波混频信号与泵浦激光进行和频,产生了位于可见光范围内的可调谐的和频信号,并从和频信号中观察到频率为608 cm 1的量子拍.结果表明,六波混频信号中的量子拍能够用于研究原子和分子的相干特性.     

From Vlasov–Poisson to Korteweg–de Vries and Zakharov–Kuznetsov

We introduce a long wave scaling for the Vlasov–Poisson equation and derive, in the cold ions limit, the Korteweg–de Vries equation (in 1D) and the Zakharov–Kuznetsov equation (in higher dimensions, in the presence of an external magnetic field). The proofs are based on the relative entropy method.     

Ion‐Acoustic Waves Instability in a Three Components Magneto‐Plasma with Nonthermal Electrons

A theoretical investigation has been made on obliquely propagating ion‐acoustic (IA) solitary structures in a three components magneto‐plasma containing cold inertial ions, Boltzmann distributed positrons, and hot non‐thermal electrons. The Zakharov‐Kuznetsov equation has been derived by the reductive perturbation method, and its solitary wave solution has been analyzed. Multi‐dimensional instability has also studied by the small‐k (long wave‐length plane wave) perturbation expansion technique, which is found to exist in such a plasma. The effects of the external magnetic field, nonthermal electrons, obliqueness and temperature ratio have significantly modified the basic properties of small but finite‐amplitude IA solitary waves, such as amplitude, width, instability criterion and the growth rate. The present investigation contributes to the physics of the nonlinear IA waves in space and laboratory electron‐positron‐ion magneto‐plasmas in which wave damping produces an electron tail. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Compact equation for gravity waves on deep water

Using the fact of vanishing four waves interaction for water gravity waves for 2D potential fluid, we have significantly simplified the well-known but cumbersome Zakharov equation. The Hamiltonian of the obtained equation is very simple and includes only the fourth order nonlinear term. It raises the question of the integrability of free surface hydrodynamics. This new equation is very suitable both for analytic study and for numerical simulation.     

Generalized Strichartz Estimates and Scattering for 3D Zakharov System

We obtain scattering for the 3D Zakharov system with non-radial small data in the energy space with angular regularity of degree one. The main ingredient is a generalized Strichartz estimate for the Schrödinger equation in the space of L ² angular integrability.     

Minimum total noise is a measure of higher order squeezing

The possibility of observing higher order squeezing in different optical processes, such as six-wave mixing and four-wave mixing, has been studied and it is shown that amplitude squared squeezing appears in all these cases. It is also shown that the minimum total noise (T_min) of a higher order squeezed state, which is a measure of the total fluctuations in the field amplitude, always increases with the increase in depth of nonclassicality associated with higher order squeezing. Thus we can use T_min as an indirect measure of higher order squeezing.     

Multi-dimensional instability of electrostatic solitary waves in ultra-relativistic degenerate electron-positron-ion plasmas

The basic features and multi-dimensional instability of electrostatic (EA) solitary waves propagating in an ultra-relativistic degenerate dense magnetized plasma (containing inertia-less electrons, inertia-less positrons, and inertial ions) have been theoretically investigated by reductive perturbation method and small-k perturbation expansion technique. The Zakharov-Kuznetsov (ZK) equation has been derived, and its numerical solutions for some special cases have been analyzed to identify the basic features (viz. amplitude, width, instability, etc.) of these electrostatic solitary structures. The implications of our results in some compact astrophysical objects, particularly white dwarfs and neutron stars, are briefly discussed.     

New exact travelling wave solutions of the generalized zakharov equations

A direct algebraic method is introduced for constructing exact travelling wave solutions of nonlinear partial differential equations with complex phases. The scheme is implemented for obtaining multiple soliton solutions of the generalized Zakharov equations, and then new exact travelling wave solutions with complex phases are obtained. In addition, by using new exact solutions of an auxiliary ordinary differential equation, new exact travelling wave solutions for the generalized Zakharov equations are obtained.     

Exact Three-Dimensional Relativistic Equation for qq Bound states

Starting with the QCD generating functional, a new derivation and a new form of the Dirac-Schriidinger (D-S) equation,catisfied by the equal-time Bethe-Salpeter amplitude of quark-antiquark bound states have been given. In this equation, the effective interaction kernel has a compact expression and can be directly calculated by means of the conventional QCD Feynman rules. F'urthermore, an equivalent reduction of the above equation to a Pauli-Schriidinger equation has also been achieved and a closed form of the effective interaction Hamiltonian appearing in the latter equation has been explicitly written out.     

Effect of Second Nonthermal Ion on the Characteristics of Dust Acoustic Solitary Waves in a Magnetized Dusty Plasma with Variable Dust Charge

The nonlinear dust acoustic solitary waves in a magnetized dusty plasma with nonthermal ions and variable dust electric charge is studied analytically. Using reductive perturbation method the Zakharov‐Kuznetsov (ZK) equation is derived and effect of nonthermal coefficient, external magnetic field, and variable dust electric charge on the amplitude and width of soliton in dusty plasma is investigated. With increasing the rate of dust charge variation with respect of plasma potential, the amplitude of generated solitary waves in magnetized dusty plasma increases to a constant magnitude while its width decreases. Increasing the nonthermal ions coefficient leads to a noticeable decrease in the amplitude of solitons while the width of soliton increases. The amplitude of generated solitary waves in such a dusty plasma is independent of applied external magnetic field but we will have more localized solitons with increasing the external magnetic field strength. It is found that solitons are strongly influenced by the direction of external magnetic field. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

非均匀交换各向异性铁磁介质的非线性表面自旋波

利用Landau-Lifshitz 方程，研究了具有非均匀交换各向异性的半无限大铁磁体的非线性表 面自旋波理论。导出了部分钉扎纯交换铁磁介质的磁化强度所满足的边界条件和非线性表面 自旋波的色散关系，并获得了自旋波振幅沿z方向驻波的一维非线性Schrdinger方程和包 络振幅沿平面传播的二维非线性Schrdinger方程，结果表明铁磁体磁化强度的包络振幅随时空变化的性质是由二维非线性Schrdinger方程决定的。因此预言铁磁介质的表面非线性激发应是二维孤波的形式。对于弱非线性表面自旋波，对非线性Schrdinger方程存在孤子形式解的可能性作了讨论. 关键词： 表面自旋波 Landau-Lifshitz方程 非线性Schrdinger方程 孤子     

The KP and ZK equations for electrostatic waves with grain charge fluctuation

The propagation of three-dimensional nonlinear dust-acoustic and dust-Coulomb waves in unmagnetized/magnetized dusty plasmas consisting of electrons, ions, and charged dust particles is investigated. The grain charge fluctuation effect is also incorporated through the current balance equation. By using the perturbation method, a Kadomtsev－Petviashvili equation and a Zakharov－Kuznetsov equation governing the nonlinear waves in the unmagnetized and magnetized systems are obtained respectively. It has been shown that with the combined effects of grain charge fluctuation, the transverse perturbation, and the external magnetic field would modify the wave structures. Waves in those systems are unstable to the high-order long-wave perturbations.     

Propagation of localized waves in magnetized cold hadronic gas

Propagation of solitary waves and their stability conditions in a cold dense hadron gas as a non-relativistic fluid is investigated based on the ‘reductive perturbation method’, at the presence of sufficiently strong external magnetic field. We have shown that the magnetic field stabilizes breaking and shock waves into livelong solitonic profiles with small amplitudes which are governed by the Zakharov–Kuznetsov (ZK) equation. Our results show that the phase speed and amplitude of solitary waves corresponding to each kind of medium components are different. The effects of medium characters on the evolution of solitary profiles are investigated too.     

On the Nikolaev-Zakharov-Zoller form for the BFKL pomeron

The equation proposed by N.N. Nikolaev, B.G. Zakharov and V.R. Zoller for the colour dipole cross-section is compared with the BFKL equation for the hard pomeron for theSU(2) colour group. It is demonstrated that for a fixed coupling constant the difference between the two equations is due to a different manner to introduce the gluon mass.     

纯永磁波荡器基波与谐波磁场的三维计算与测试

 对标淮的纯永磁波荡器进行了三维磁场的有限元计算,给出了纯永磁波荡器的基波与谐波磁场的幅值与相位,并与测试结果进行对比,结果表明,标准的纯永磁波荡器谐波磁场幅值比基波幅值低两个数量级。     

Statistical properties of random environment of 1<Emphasis Type="Italic">D</Emphasis> quantum <Emphasis Type="Italic">N</Emphasis>-particles system in external field

The investigation of 1D quantum N-particle system (PS) with relaxation in the random environment under the influence of external field is conducted within the framework of the stochastic differential equation of the Langevin—Schrödinger (L—Sch) type. Using L—Sch equation, the 2D second-order nonstationary partial differential equation is found, which describes the quantum distribution in the environment, depending on the energy of nonperturbed 1D quantum N-PS and on the external field parameters. It is shown that the average value of the interaction potential between 1D disordered quantum N-PS and the external field, has the ultraviolet divergence. This problem is solved by the renormalization of the equation for the function of quantum distribution. It is shown that it has a sense of dimensional renormalization which is characteristic for the quantum field theory. Critical properties of the environment are investigated in detail. The possibility of the first-order phase transition in the environment distribution depending on amplitude of an external field is been shown.