In this paper, the approximate expressions of the solitary wave solutions for a class of nonlinear disturbed long-wave system are constructed using the homotopie mapping method.
Based on phase-plane orbit analysis, the mathematical model of piecewise-smooth systems of multi-degree-of-freedom under the mode coordinate is established. Approximate analytical solution under the physical coordinat...Based on phase-plane orbit analysis, the mathematical model of piecewise-smooth systems of multi-degree-of-freedom under the mode coordinate is established. Approximate analytical solution under the physical coordinate of multi-degree-of-freedom self-excited vibration induced by dry friction of piecewise-smooth nonlinear systems is derived by means of average method, the results of which agree with those of the numerical solution. An effective and reliable analytical method investigating piecewise-smooth nonlinear systems of multi-degree-of-freedom has been given. Furthermore, this paper qualitatively analyses the curves about stationary amplitude versus rubbing velocity of hands and versus natural frequency of hands, and about angular frequency versus rubbing velocity of hands. The results provide a theoretical basis for identifying parameters of the system and the analysis of steady region.展开更多
In this paper an efficient computational method based on extending the sensitivity approach(SA) is proposed to find an analytic exact solution of nonlinear differential difference equations.In this manner we avoid sol...In this paper an efficient computational method based on extending the sensitivity approach(SA) is proposed to find an analytic exact solution of nonlinear differential difference equations.In this manner we avoid solving the nonlinear problem directly.By extension of sensitivity approach for differential difference equations(DDEs),the nonlinear original problem is transformed into infinite linear differential difference equations,which should be solved in a recursive manner.Then the exact solution is determined in the form of infinite terms series and by intercepting series an approximate solution is obtained.Numerical examples are employed to show the effectiveness of the proposed approach.展开更多
An analytic approximation method known as the homotopy analysis method(HAM)is applied to study the nonlinear hydroelastic progressive waves traveling in an infinite elastic plate such as an ice sheet or a very large f...An analytic approximation method known as the homotopy analysis method(HAM)is applied to study the nonlinear hydroelastic progressive waves traveling in an infinite elastic plate such as an ice sheet or a very large floating structure(VLFS)on the surface of deep water.A convergent analytical series solution for the plate deflection is derived by choosing the optimal convergencecontrol parameter.Based on the analytical solution the efects of diferent parameters are considered.We find that the plate deflection becomes lower with an increasing Young’s modulus of the plate.The displacement tends to be flattened at the crest and be sharpened at the trough as the thickness of the plate increases,and the larger density of the plate also causes analogous results.Furthermore,it is shown that the hydroelastic response of the plate is greatly afected by the high-amplitude incident wave.The results obtained can help enrich our understanding of the nonlinear hydroelastic response of an ice sheet or a VLFS on the water surface.展开更多
Unified analytical solutions are presented for the predictions of the stresses and displacements around a circular opening based on nonqinear unified failure criterion and the elastic-brittle-plastic softening model. ...Unified analytical solutions are presented for the predictions of the stresses and displacements around a circular opening based on nonqinear unified failure criterion and the elastic-brittle-plastic softening model. Unified analytical solutions not only involve generally traditional solutions which are based on the Hock-Brown （H-B） failure criterion or the non-linear twin-shear failure criterion, but also involve other new results. The results of the radius of plastic zone, radial displacements and stresses are obviously different using three rock masses when different values of the unified failure criterion parameter or different material behavior models are used. For a given condition, the radius of plastic zone and radial displacements are reduced by increasing the unified failure criterion parameter. The latent potentialities of rock mass result from considering the effect of intermediate principal stress. It is shown that proper choices of the failure criterion and the material behavior model for rock mass are significant in the tunnel design.展开更多
Both the homotopy analysis method and Galerkin spectral method are applied to find the analytical solutions of the two-dimensional and time-independent Gross-Pitaevskii equation, a nonlinear Schrodinger equation used ...Both the homotopy analysis method and Galerkin spectral method are applied to find the analytical solutions of the two-dimensional and time-independent Gross-Pitaevskii equation, a nonlinear Schrodinger equation used in describing the system of Bose-Einstein condensates trapped in a harmonic potential. The approximate analytical solutions are obtained successfully. Comparisons between the analytical solutions and the numerical solutions have been made. The results indicate that they are agreement very well with each other when the atomic interaction is not too strong.展开更多
We investigate analytical solutions of the(2+1)-dimensional combining cubic-quintic nonlinear Schrdinger(CQNLS) equation by the classical Lie group symmetry method.We not only obtain the Lie-point symmetries and some(...We investigate analytical solutions of the(2+1)-dimensional combining cubic-quintic nonlinear Schrdinger(CQNLS) equation by the classical Lie group symmetry method.We not only obtain the Lie-point symmetries and some(1+1)-dimensional partial differential systems,but also derive bright solitons,dark solitons,kink or anti-kink solutions and the localized instanton solution.展开更多
基金Supported by the National Natural Science Foundation of China under Grant No.40876010the Main Direction Program of the Knowledge Innovation Project of Chinese Academy of Sciences under Grant No.KZCX2-YW-Q03-08+2 种基金the LASG State Key Laboratory Special Fundthe Foundation of Shanghai Municipal Education Commission under Grant No.E03004the Natural Science Foundation of Zhejiang Province under Grant No.Y6090164
文摘In this paper, the approximate expressions of the solitary wave solutions for a class of nonlinear disturbed long-wave system are constructed using the homotopie mapping method.
文摘Based on phase-plane orbit analysis, the mathematical model of piecewise-smooth systems of multi-degree-of-freedom under the mode coordinate is established. Approximate analytical solution under the physical coordinate of multi-degree-of-freedom self-excited vibration induced by dry friction of piecewise-smooth nonlinear systems is derived by means of average method, the results of which agree with those of the numerical solution. An effective and reliable analytical method investigating piecewise-smooth nonlinear systems of multi-degree-of-freedom has been given. Furthermore, this paper qualitatively analyses the curves about stationary amplitude versus rubbing velocity of hands and versus natural frequency of hands, and about angular frequency versus rubbing velocity of hands. The results provide a theoretical basis for identifying parameters of the system and the analysis of steady region.
文摘In this paper an efficient computational method based on extending the sensitivity approach(SA) is proposed to find an analytic exact solution of nonlinear differential difference equations.In this manner we avoid solving the nonlinear problem directly.By extension of sensitivity approach for differential difference equations(DDEs),the nonlinear original problem is transformed into infinite linear differential difference equations,which should be solved in a recursive manner.Then the exact solution is determined in the form of infinite terms series and by intercepting series an approximate solution is obtained.Numerical examples are employed to show the effectiveness of the proposed approach.
基金supported by the National Natural Science Foundation of China (Grant No. 11072140)
文摘An analytic approximation method known as the homotopy analysis method(HAM)is applied to study the nonlinear hydroelastic progressive waves traveling in an infinite elastic plate such as an ice sheet or a very large floating structure(VLFS)on the surface of deep water.A convergent analytical series solution for the plate deflection is derived by choosing the optimal convergencecontrol parameter.Based on the analytical solution the efects of diferent parameters are considered.We find that the plate deflection becomes lower with an increasing Young’s modulus of the plate.The displacement tends to be flattened at the crest and be sharpened at the trough as the thickness of the plate increases,and the larger density of the plate also causes analogous results.Furthermore,it is shown that the hydroelastic response of the plate is greatly afected by the high-amplitude incident wave.The results obtained can help enrich our understanding of the nonlinear hydroelastic response of an ice sheet or a VLFS on the water surface.
基金Project (No.SJ08E204) supported by the Natural Science Foundation of Shanxi Province,China
文摘Unified analytical solutions are presented for the predictions of the stresses and displacements around a circular opening based on nonqinear unified failure criterion and the elastic-brittle-plastic softening model. Unified analytical solutions not only involve generally traditional solutions which are based on the Hock-Brown （H-B） failure criterion or the non-linear twin-shear failure criterion, but also involve other new results. The results of the radius of plastic zone, radial displacements and stresses are obviously different using three rock masses when different values of the unified failure criterion parameter or different material behavior models are used. For a given condition, the radius of plastic zone and radial displacements are reduced by increasing the unified failure criterion parameter. The latent potentialities of rock mass result from considering the effect of intermediate principal stress. It is shown that proper choices of the failure criterion and the material behavior model for rock mass are significant in the tunnel design.
基金Supported by the National Natural Science Foundation under Grant No. 11047010
文摘Both the homotopy analysis method and Galerkin spectral method are applied to find the analytical solutions of the two-dimensional and time-independent Gross-Pitaevskii equation, a nonlinear Schrodinger equation used in describing the system of Bose-Einstein condensates trapped in a harmonic potential. The approximate analytical solutions are obtained successfully. Comparisons between the analytical solutions and the numerical solutions have been made. The results indicate that they are agreement very well with each other when the atomic interaction is not too strong.
基金Supported by the National Natural Science Foundation of China under Grant Nos. 10875106 and 11175158
文摘We investigate analytical solutions of the(2+1)-dimensional combining cubic-quintic nonlinear Schrdinger(CQNLS) equation by the classical Lie group symmetry method.We not only obtain the Lie-point symmetries and some(1+1)-dimensional partial differential systems,but also derive bright solitons,dark solitons,kink or anti-kink solutions and the localized instanton solution.
