One-dimensional generalized Boussinesq equation u tt-u xx＋（f（u）＋u xx）xx=0.with periodic boundary condition is considered, where f（u） = u3. First, the above equation is written as a Hamiltonian system, and then...One-dimensional generalized Boussinesq equation u tt-u xx＋（f（u）＋u xx）xx=0.with periodic boundary condition is considered, where f（u） = u3. First, the above equation is written as a Hamiltonian system, and then by choosing the eigenfunctions of the linear operator as bases, the Hamiltonian system in the coordinates is expressed. Because of the intricate resonance between the tangential frequencies and normal frequencies, some quasi-periodic solutions with special structures are considered. Secondly, the regularity of the Hamiltonian vector field is verified and then the fourth-order terms are normalized. By the Birkhoff normal form, the non- degeneracy and non-resonance conditions are obtained. Applying the infinite dimensional Kolmogorov-Arnold-Moser （KAM） theorem, the existence of finite dimensional invariant tori for the equivalent Hamiltonian system is proved. Hence many small-amplitude quasi-periodic solutions for the above equation are obtained.展开更多
China faces the challenge of calming white-hot house prices and preventing bubble bursts across the country Nearly two years after the financial crisis,the Chinese economy is faring well-maybe too well.A recent Minist...China faces the challenge of calming white-hot house prices and preventing bubble bursts across the country Nearly two years after the financial crisis,the Chinese economy is faring well-maybe too well.A recent Ministry of Land and Resources (MLR) report stated a展开更多
基金The National Natural Science Foundation of China(No.11301072)the Natural Science Foundation of Jiangsu Province(No.BK20131285)the Research and Innovation Project for College Graduates of Jiangsu Province(No.CXZZ12-0083,CXLX13-074)
文摘One-dimensional generalized Boussinesq equation u tt-u xx＋（f（u）＋u xx）xx=0.with periodic boundary condition is considered, where f（u） = u3. First, the above equation is written as a Hamiltonian system, and then by choosing the eigenfunctions of the linear operator as bases, the Hamiltonian system in the coordinates is expressed. Because of the intricate resonance between the tangential frequencies and normal frequencies, some quasi-periodic solutions with special structures are considered. Secondly, the regularity of the Hamiltonian vector field is verified and then the fourth-order terms are normalized. By the Birkhoff normal form, the non- degeneracy and non-resonance conditions are obtained. Applying the infinite dimensional Kolmogorov-Arnold-Moser （KAM） theorem, the existence of finite dimensional invariant tori for the equivalent Hamiltonian system is proved. Hence many small-amplitude quasi-periodic solutions for the above equation are obtained.
文摘China faces the challenge of calming white-hot house prices and preventing bubble bursts across the country Nearly two years after the financial crisis,the Chinese economy is faring well-maybe too well.A recent Ministry of Land and Resources (MLR) report stated a
