Inverse scattering method and soliton solutionfamily for the Einstein--Maxwell theory with multiple Abelian gauge fields

A Hauser-Ernst-type extended hyperbolic complex linear system given in our previous paper [Gao Y J 2004 Chin. Phys. 13 602] is slightly modified and used to develop a new inverse scattering method for the stationary axisymmetric Einstein-Maxwell theory with multiple Abelian gauge fields. The reduction procedures in this inverse scattering method are found to be fairly simple, which makes the inverse scattering method be fine and effective in practical application. As an example, a concrete family of soliton solutions for the considered theory is obtained.     

Adomian decomposition method and Padé approximants for solving the Blaszak--Marciniak lattice

The Adomian decomposition method （ADM） and Pade approximants are combined to solve the well-known Blaszak-Marciniak lattice, which has rich mathematical structures and many important applications in physics and mathematics. In some cases, the truncated series solution of ADM is adequate only in a small region when the exact solution is not reached. To overcome the drawback, the Pade approximants, which have the advantage in turning the polynomials approximation into a rational function, are applied to the series solution to improve the accuracy and enlarge the convergence domain. By using the ADM-Pade technique, the soliton solutions of the Blaszak-Marciniak lattice are constructed with better accuracy and better convergence than by using the ADM alone. Numerical and figurative illustrations show that it is a promising tool for solving nonlinear problems.     

Soliton squeezing generated in an all-fiber contiguration

We experimentally demonstrate amplitude squeezed soliton utilizing intensity-dependent self-phase modulation in an asymmetric Sagnac interferometer.The system.whose components are connected via ferrule connector/physical connection(FC/PC)fiber connectors,constitutes all-fiber configuration to generate squeezed soliton.Soliton amplitude reduction measured by homodyne detection is near 4.0 dB below the shot-noise level.Optimal squeezing fields in both simple and compact all-fiber configuration are obtained.     

掺锗硅基高非线性光纤超连续光源研究

利用非线性偏振旋转锁模掺铒光纤激光器和1100m长的掺锗硅基高非线性光纤制作了超连续光源，获得了从1150～1750nm的超宽带输出光谱，其中1150～1350nm波段光谱起伏小于3dB，1600～1700nm波段平坦度优于1dB，并有很好的向长波延展空间。光谱展宽的机理为孤子分裂与受激拉曼散射，而四波混频使光谱进一步展宽。     

Soliton solution and interaction property for a coupled modified Korteweg-de Vries （mKdV） system

Hirota＇s bilinear direct method is applied to constructing soliton solutions to a special coupled modified Korteweg- de Vries （mKdV） system. Some physical properties such as the spatiotemporal evolution, waveform structure, interactive phenomena of solitons are discussed, especially in the two-soliton case. It is found that different interactive behaviours of solitary waves take place under different parameter conditions of overtaking collision in this system. It is verified that the elastic interaction phenomena exist in this （1＋1）-dimensional integrable coupled model.     

Double-Alekseev inverse scattering method in the stationary axi-symmetric vacuum gravitation field equations

We present a new improvement to the Alekseev inverse scattering method. This improved inverse scattering method is extended to a double form, followed by the generation of some new solutions of the double-complex Kinnersley equations. As the double-complex function method contains the Kramer-Neugebauer substitution and analytic continuation, a pair of real gravitation soliton solutions of the Einstein’s field equations can be obtained from a double N-soliton solution. In the case of the flat Minkowski space background solution, the general formulas of the new solutions are presented.      

Abundant Multisoliton Structure of (3+1)-Dimensional Breaking Soliton Equation

Using the extended homogeneous balance method, we obtained abundant exact solution structures of the (3 1 )-dimensional breaking soliton equation. By means of the leading order term analysis, the nonlinear transformations of the (3t1)-dimensional breaking soliton equation are given first, and then some special types of single solitary wave solutions and the multisoliton solutions are constructed.     

Solitons and Fractal Kerr Response

Optical solitary waves that propagate in a Kerr medium exhibiting a power-law nonlocal response are studied analytically. The first-principles stability analysis based on quantum field theory shows that within the whole range of the exponent (the fractal dimension) the solitary wave can be stabilized.     

饱和光纤中的各阶孤子及孤子相互作用

首先研究了非线性饱和光纤中各阶孤子存在的幅值范围，与标准非饱和情况的非线性薛定谔孤子非常不同，即一阶孤子幅值范围是１．４≤Ｎ≤∵．０，二阶孤子为４．０≤Ｎ≤♀．０，三阶孤子为７．０≤Ｎ≤≤１５．０，并分析了各阶孤子的传输特性，最后研究了双一阶孤子相作用的若干特点，明确了五个方面的特性。     

Dark Multi-Soliton Solution of the Nonlinear Schrödinger Equation with Non-Vanishing Boundary

The inverse scattering transform for the nonlinear Schrödinger equation in normal dispersion with non-vanishing boundary values is re-examined using an affine parameter to avoid double-valued functions. An operable algebraic procedure is developed to evaluate dark multi-soliton solutions. The dark two-soliton solution is given explicitly as an example, and is verified by direct substitution. The additional motion of the soliton center is given by its asymptotic behavior.