A generalized hyperbolic perturbation method is presented for homoclinic solutions of strongly nonlinear autonomous oscillators, in which the perturbation proce- dure is improved for those systems whose exact homoclin...A generalized hyperbolic perturbation method is presented for homoclinic solutions of strongly nonlinear autonomous oscillators, in which the perturbation proce- dure is improved for those systems whose exact homoclinic generating solutions cannot be explicitly derived. The generalized hyperbolic functions are employed as the basis functions in the present procedure to extend the validity of the hyperbolic perturbation method. Several strongly nonlinear oscillators with quadratic, cubic, and quartic nonlinearity are studied in detail to illustrate the efficiency and accuracy of the present method.展开更多
New two-component vector breather solution of the modified Benjamin-Bona-Mahony(MBBM)equation is considered.Using the generalized perturbation reduction method,the MBBM equation is reduced to the coupled nonlinear Sch...New two-component vector breather solution of the modified Benjamin-Bona-Mahony(MBBM)equation is considered.Using the generalized perturbation reduction method,the MBBM equation is reduced to the coupled nonlinear Schr¨odinger equations for auxiliary functions.Explicit analytical expressions for the profile and parameters of the vector breather oscillating with the sum and difference of the frequencies and wavenumbers are presented.The two-component vector breather and single-component scalar breather of the MBBM equation is compared.展开更多
基金Project supported by the National Natural Science Foundation of China (Nos. 10972240 and 11102045)the Natural Science Foundation of Guangdong Province of China (No. S20110400040)+2 种基金the Foundation of Guangdong Education Department of China (No. LYM10108)the Foundation of Guangzhou Education Bureau of China (No. 10A024)the Research Grant Council of Hong Kong of China (No. GRF-HKU-7173-09E)
文摘A generalized hyperbolic perturbation method is presented for homoclinic solutions of strongly nonlinear autonomous oscillators, in which the perturbation proce- dure is improved for those systems whose exact homoclinic generating solutions cannot be explicitly derived. The generalized hyperbolic functions are employed as the basis functions in the present procedure to extend the validity of the hyperbolic perturbation method. Several strongly nonlinear oscillators with quadratic, cubic, and quartic nonlinearity are studied in detail to illustrate the efficiency and accuracy of the present method.
文摘New two-component vector breather solution of the modified Benjamin-Bona-Mahony(MBBM)equation is considered.Using the generalized perturbation reduction method,the MBBM equation is reduced to the coupled nonlinear Schr¨odinger equations for auxiliary functions.Explicit analytical expressions for the profile and parameters of the vector breather oscillating with the sum and difference of the frequencies and wavenumbers are presented.The two-component vector breather and single-component scalar breather of the MBBM equation is compared.
