Stationary even periodic solutions of the Swift-Hohenberg equation areanalyzed for the critical parameter k = 1, and it is proved that there exist periodic solutionshaving the same energy as the constant solution u = ...Stationary even periodic solutions of the Swift-Hohenberg equation areanalyzed for the critical parameter k = 1, and it is proved that there exist periodic solutionshaving the same energy as the constant solution u = 0. For k ≤ 0, some qualitative properties ofthe solutions are also proved.展开更多
By using the general solutions of a new coupled Riccati equations, a direct algebraic method is described to construct doubly periodic solutions (Jacobi elliptic function solution) for the coupled nonlinear Klein-Gord...By using the general solutions of a new coupled Riccati equations, a direct algebraic method is described to construct doubly periodic solutions (Jacobi elliptic function solution) for the coupled nonlinear Klein-Gordon equations.It is shown that more doubly periodic solutions and the corresponding solitary wave solutions and trigonometric function solutions can be obtained in a unified way by this method.展开更多
文摘Stationary even periodic solutions of the Swift-Hohenberg equation areanalyzed for the critical parameter k = 1, and it is proved that there exist periodic solutionshaving the same energy as the constant solution u = 0. For k ≤ 0, some qualitative properties ofthe solutions are also proved.
文摘By using the general solutions of a new coupled Riccati equations, a direct algebraic method is described to construct doubly periodic solutions (Jacobi elliptic function solution) for the coupled nonlinear Klein-Gordon equations.It is shown that more doubly periodic solutions and the corresponding solitary wave solutions and trigonometric function solutions can be obtained in a unified way by this method.
