Solitary and Periodic Gravity-Capillary Waves of Finite Amplitude,

摘要: Two-dimensional solitary and periodic waves in water of finite depth are considered. The propagate under the combined influence gravity surface tension. flow, profile phase velocity functions amplitude wave parameters l = λ/ H τ T /ρ gH 2 . Here λ is wavelength, depth, tension, ρ density g acceleration due to gravity. For $\dot{\tau} >\frac{1}{3}$ , large values small amplitude, satisfies Korteweg–de Vries equation approximately. However, for close $\frac{1}{3}$ this becomes invalid. In present paper a new valid 1/3 obtained. Moreover, numerical scheme based on an integrodifferential-equation formulation derived solve problem fully nonlinear case. Accurate solutions presented. results show that does not provide accurate description gravity-capillary $\tau addition, it shown elevation cannot be obtained as continuous limit wavelength tends infinity. Graphs included.