It is found with the method of multiple scales that there exists a new periodical processwith long period T_1= 2π(Δω~2-f^2ω)^(1/2) when f= ω_e^2A_r/g and Δω/ω=ω-ω_e/ω are O(ε), whereg is the gravitational ...It is found with the method of multiple scales that there exists a new periodical processwith long period T_1= 2π(Δω~2-f^2ω)^(1/2) when f= ω_e^2A_r/g and Δω/ω=ω-ω_e/ω are O(ε), whereg is the gravitational acceleration, ω_e half of the driving frequency, A. the driving ampli-tude, ω the frequency of (0, 1) mode of the water trough. Suggest that φ which is corre-lativc with the complex amplitude of velocity potential is a function of θ and ?φ/?θ is O(ω~3),where θ satisfies θ(t + T_1) =θ(t), e.g. θ=?/Ω sinΩ_t (Ω=2π/T_1). The NLS equation of theφ(x,θ) is obtained. The phenomena of passing--through and oscil- lating about each other ofa pair of solitary waves in a rectangular water trough can be explained.展开更多
基金Project supported by the National Natural Science Foundation of China
文摘It is found with the method of multiple scales that there exists a new periodical processwith long period T_1= 2π(Δω~2-f^2ω)^(1/2) when f= ω_e^2A_r/g and Δω/ω=ω-ω_e/ω are O(ε), whereg is the gravitational acceleration, ω_e half of the driving frequency, A. the driving ampli-tude, ω the frequency of (0, 1) mode of the water trough. Suggest that φ which is corre-lativc with the complex amplitude of velocity potential is a function of θ and ?φ/?θ is O(ω~3),where θ satisfies θ(t + T_1) =θ(t), e.g. θ=?/Ω sinΩ_t (Ω=2π/T_1). The NLS equation of theφ(x,θ) is obtained. The phenomena of passing--through and oscil- lating about each other ofa pair of solitary waves in a rectangular water trough can be explained.
