In this paper, two (3+1)-dimensional equations are investigated.Auto-Baecklund transformation is obtained, which is used with some ansatze to seek new types ofexact solutions including some arbitrary functions. When t...In this paper, two (3+1)-dimensional equations are investigated.Auto-Baecklund transformation is obtained, which is used with some ansatze to seek new types ofexact solutions including some arbitrary functions. When these arbitrary functions are taken assome special functions, these solutions possess abundant structures. These solutions containsoliton-like solutions and rational solutions.展开更多
By using an extended Melnikov method on multi-degree-of-freedom Hamiltonian systems with perturbations,the global bifurcations and chaotic dynamics are investigated for a parametrically excited,simply supported rectan...By using an extended Melnikov method on multi-degree-of-freedom Hamiltonian systems with perturbations,the global bifurcations and chaotic dynamics are investigated for a parametrically excited,simply supported rectangular buckled thin plate.The formulas of the rectangular buckled thin plate are derived by using the von Karman type equation.The two cases of the buckling for the rectangular thin plate are considered.With the aid of Galerkin's approach,a two-degree-of-freedom nonautonomous nonlinear system is obtained for the non-autonomous rectangular buckled thin plate.The high-dimensional Melnikov method developed by Yagasaki is directly employed to the non-autonomous ordinary differential equation of motion to analyze the global bifurcations and chaotic dynamics of the rectangular buckled thin plate.Numerical method is used to find the chaotic responses of the non-autonomous rectangular buckled thin plate.The results obtained here indicate that the chaotic motions can occur in the parametrically excited,simply supported rectangular buckled thin plate.展开更多
文摘In this paper, two (3+1)-dimensional equations are investigated.Auto-Baecklund transformation is obtained, which is used with some ansatze to seek new types ofexact solutions including some arbitrary functions. When these arbitrary functions are taken assome special functions, these solutions possess abundant structures. These solutions containsoliton-like solutions and rational solutions.
基金supported by the National Natural Science Foundation of China (Grant Nos. 11072008,10732020 and 11002005)the Funding Project for Academic Human Resources Development in Institutions of Higher Learning under the Jurisdiction of Beijing Municipality(PHRIHLB)
文摘By using an extended Melnikov method on multi-degree-of-freedom Hamiltonian systems with perturbations,the global bifurcations and chaotic dynamics are investigated for a parametrically excited,simply supported rectangular buckled thin plate.The formulas of the rectangular buckled thin plate are derived by using the von Karman type equation.The two cases of the buckling for the rectangular thin plate are considered.With the aid of Galerkin's approach,a two-degree-of-freedom nonautonomous nonlinear system is obtained for the non-autonomous rectangular buckled thin plate.The high-dimensional Melnikov method developed by Yagasaki is directly employed to the non-autonomous ordinary differential equation of motion to analyze the global bifurcations and chaotic dynamics of the rectangular buckled thin plate.Numerical method is used to find the chaotic responses of the non-autonomous rectangular buckled thin plate.The results obtained here indicate that the chaotic motions can occur in the parametrically excited,simply supported rectangular buckled thin plate.
