In the present paper,with the aid of symbolic computation,families of new nontrivial solutions of thefirst-order sub-ODE F′~2=AF^2+BF^(2+p)+CF^(2+2p)(where F'=dF/dξ,p>0)are obtained.To our best knowledge,thes...In the present paper,with the aid of symbolic computation,families of new nontrivial solutions of thefirst-order sub-ODE F′~2=AF^2+BF^(2+p)+CF^(2+2p)(where F'=dF/dξ,p>0)are obtained.To our best knowledge,these nontrivial solutions have not been found in[X.Z.Li and M.L.Wang,Phys.Lett.A 361(2007)115]and[S.Zhang,W.Wang,and J.L.Tong,Phys.Lett.A 372(2008)3808]and other existent papers until now.Using thesenontrivial solutions,the sub-ODE method is described to construct several kinds of exact travelling wave solutions for thegeneralized KdV-mKdV equation with higher-order nonlinear terms and the generalized ZK equation with higher-ordernonlinear terms.By means of this method,many other physically important nonlinear partial differential equations withnonlinear terms of any order can be investigated and new nontrivial solutions can be explicitly obtained with the helpof symbolic computation system Maple or Mathematica.展开更多
The higher order asymptotic fields at the tip of a sharp V-notchin a power-hardening material for plane strain problem of Mode I arederived. The order hierarchy in powers of r for various hardeningexponents n and notc...The higher order asymptotic fields at the tip of a sharp V-notchin a power-hardening material for plane strain problem of Mode I arederived. The order hierarchy in powers of r for various hardeningexponents n and notch angles β is obtained. The angulardistributions of stress for several cases are plotted. Theself-similarity behavior between the higher order terms is noticed.It is found that the terms with higher Order can be neglected for theV-notch angle β>45°.展开更多
On the basis of an introduction of the Wigner Higher-Order spectra (WHOS) and a general class of time-frequency higher-order moment spectra, the geophysical signal was analyzed using the higher order time-frequency di...On the basis of an introduction of the Wigner Higher-Order spectra (WHOS) and a general class of time-frequency higher-order moment spectra, the geophysical signal was analyzed using the higher order time-frequency distributions (TFD). Simulation results obtained in this paper show that the higher-order TFD (Wigner Bispectrum, Wigner Trispectrum and Choi-Williams Trispectrum) have much better Time-Frequency Concentration than the second-order TFD, and the reduced interference higher-order TFD such as CWT can effectively reduce the cross-term in multicomponent signals and simultaneously obtain high time-frequency concentration.展开更多
This paper mainly deals with the higher-order coupled Kirchhoff-type equations with nonlinear strong damped and source terms in a bounded domain. We obtain some results that are estimation of the upper bounds of Hausd...This paper mainly deals with the higher-order coupled Kirchhoff-type equations with nonlinear strong damped and source terms in a bounded domain. We obtain some results that are estimation of the upper bounds of Hausdorff dimension and Fractal dimension of the global attractor.展开更多
基于分部求和(Summation By Parts)方法和同时逼近项(Simultaneous Approximation Terms)技术建立的有限差分方法,具有更高的精度和稳定性。同时在介质几何不连续、参数突变条件具有较大的优势。国内对SBP-SAT方法的相关研究目前较少,...基于分部求和(Summation By Parts)方法和同时逼近项(Simultaneous Approximation Terms)技术建立的有限差分方法,具有更高的精度和稳定性。同时在介质几何不连续、参数突变条件具有较大的优势。国内对SBP-SAT方法的相关研究目前较少,论文对该方法的研究背景,方法发展过程进行了介绍并基于SBP-SAT方法和弹性波动理论,结合初边值条件,推导出曲线网格条件下的弹性波动SBP-SAT离散方程。最后,通过数值模拟实现地震波传播过程,介绍该方法在地震数值模拟领域中的应用价值和前景。展开更多
文摘In the present paper,with the aid of symbolic computation,families of new nontrivial solutions of thefirst-order sub-ODE F′~2=AF^2+BF^(2+p)+CF^(2+2p)(where F'=dF/dξ,p>0)are obtained.To our best knowledge,these nontrivial solutions have not been found in[X.Z.Li and M.L.Wang,Phys.Lett.A 361(2007)115]and[S.Zhang,W.Wang,and J.L.Tong,Phys.Lett.A 372(2008)3808]and other existent papers until now.Using thesenontrivial solutions,the sub-ODE method is described to construct several kinds of exact travelling wave solutions for thegeneralized KdV-mKdV equation with higher-order nonlinear terms and the generalized ZK equation with higher-ordernonlinear terms.By means of this method,many other physically important nonlinear partial differential equations withnonlinear terms of any order can be investigated and new nontrivial solutions can be explicitly obtained with the helpof symbolic computation system Maple or Mathematica.
基金the National Natural Science Foundation of China (Nos.10132010 and 10072033).
文摘The higher order asymptotic fields at the tip of a sharp V-notchin a power-hardening material for plane strain problem of Mode I arederived. The order hierarchy in powers of r for various hardeningexponents n and notch angles β is obtained. The angulardistributions of stress for several cases are plotted. Theself-similarity behavior between the higher order terms is noticed.It is found that the terms with higher Order can be neglected for theV-notch angle β>45°.
基金Supported by the National Natural Science Foundation of China( 4 990 40 10 )
文摘On the basis of an introduction of the Wigner Higher-Order spectra (WHOS) and a general class of time-frequency higher-order moment spectra, the geophysical signal was analyzed using the higher order time-frequency distributions (TFD). Simulation results obtained in this paper show that the higher-order TFD (Wigner Bispectrum, Wigner Trispectrum and Choi-Williams Trispectrum) have much better Time-Frequency Concentration than the second-order TFD, and the reduced interference higher-order TFD such as CWT can effectively reduce the cross-term in multicomponent signals and simultaneously obtain high time-frequency concentration.
文摘This paper mainly deals with the higher-order coupled Kirchhoff-type equations with nonlinear strong damped and source terms in a bounded domain. We obtain some results that are estimation of the upper bounds of Hausdorff dimension and Fractal dimension of the global attractor.
文摘基于分部求和(Summation By Parts)方法和同时逼近项(Simultaneous Approximation Terms)技术建立的有限差分方法,具有更高的精度和稳定性。同时在介质几何不连续、参数突变条件具有较大的优势。国内对SBP-SAT方法的相关研究目前较少,论文对该方法的研究背景,方法发展过程进行了介绍并基于SBP-SAT方法和弹性波动理论,结合初边值条件,推导出曲线网格条件下的弹性波动SBP-SAT离散方程。最后,通过数值模拟实现地震波传播过程,介绍该方法在地震数值模拟领域中的应用价值和前景。
