High-order models with a dissipative term for nonlinear and dispersive wave in water of varying depth with an arbitrary sloping bottom are presented in this article. First, the formal derivations to any high order of ...High-order models with a dissipative term for nonlinear and dispersive wave in water of varying depth with an arbitrary sloping bottom are presented in this article. First, the formal derivations to any high order of mu(= h/lambda, depth to deep-water wave length ratio) and epsilon(= a/h, wave amplitude to depth ratio) for velocity potential, particle velocity vector, pressure and the Boussinesq-type equations for surface elevation eta and horizontal velocity vector (U) over right arrow at any given level in water are given. Then, the exact explicit expressions to the fourth order of mu are derived. Finally, the linear solutions of eta, (U) over right arrow, C (phase-celerity) and C-g (group velocity) for a constant water depth are obtained. Compared with the Airy theory, excellent results can be found even for a water depth as large as the wave legnth. The present high-order models are applicable to nonlinear regular and irregular waves in water of any varying depth (from shallow to deep) and bottom slope (from mild to steep).展开更多
The approximate expressions of the travelling wave solutions for a class of nonlinear disturbed long-wave system are constructed using the generalized variational iteration method.
From April, 2003 to September, 2004, a passive broadband seismic array consisting of 60 stations was deployed over the Tianshan orogenic belt by State Key Laboratory of Earthquake Dynamics, Institute of Geology, China...From April, 2003 to September, 2004, a passive broadband seismic array consisting of 60 stations was deployed over the Tianshan orogenic belt by State Key Laboratory of Earthquake Dynamics, Institute of Geology, China Earthquake Administration. Among them, 51 stations make up an about 500-km-long profile across the Tianshan Mountains from Kuytun to Kuqa. The receiver function profile and S-wave velocity structure of the crust and upper mantle down to 100 km deep are obtained by using the re-ceiver function method (Liu et al. 1996, 2000). The main results can be summarized as follows: (1) A clear mountain root does not exist beneath the Tianshan Mountains, and the crust-mantle boundaries underneath the stations mostly have transitional structures. This implies that the material differentia-tion between the crust and mantle is not yet accomplished and the orogenic process is still going on. (2) The crust beneath the Tianshan Mountains has laterally blocked structures in direction perpendicular to the mountain strike, and the crust-mantle boundary has a clear dislocation structure. Both of them correspond to each other. (3) The offsets of the Moho discontinuity are highly correlated to the tectonic borders on the surface and that corresponding to the frontal southern Tianshan fault reaches to 14 km. This manifests that large vertical divergent movement took place between different blocks. This sup-ports the discontinuous model of the Tianshan orogeny, and the Tarim block subduction is restricted only to the southern side of the South Tianshan. (4) Inside the upper and middle crust of the Tianshan Mountains exist several low-velocity bodies correlated with high seismicity located on the moun-tain-basin jointures on both sides of the mountain and between different blocks, and the low-velocity bodies on the mountain-basin jointures are inclined obviously to the mountain. This implies that the low-velocity bodies may be correlated closely to the thrust and subduction of the basins on both sides of the mountain, the spli展开更多
From the nonlinear sine-Gordon equation, new transformations are obtained in this paper, which are applied to propose a new approach to construct exact periodic solutions to nonlinear wave equations. It is shown that ...From the nonlinear sine-Gordon equation, new transformations are obtained in this paper, which are applied to propose a new approach to construct exact periodic solutions to nonlinear wave equations. It is shown that more new periodic solutions can be obtained by this new approach, and more shock wave solutions or solitary wave solutions can be got under their limit conditions.展开更多
The elliptic equation is taken as a transformation and applied to solve nonlinear wave equations. It is shown that this method is more powerful to give more kinds of solutions, such as rational solutions, solitary wav...The elliptic equation is taken as a transformation and applied to solve nonlinear wave equations. It is shown that this method is more powerful to give more kinds of solutions, such as rational solutions, solitary wave solutions,periodic wave solutions and so on, so it can be taken as a generalized method.展开更多
文摘High-order models with a dissipative term for nonlinear and dispersive wave in water of varying depth with an arbitrary sloping bottom are presented in this article. First, the formal derivations to any high order of mu(= h/lambda, depth to deep-water wave length ratio) and epsilon(= a/h, wave amplitude to depth ratio) for velocity potential, particle velocity vector, pressure and the Boussinesq-type equations for surface elevation eta and horizontal velocity vector (U) over right arrow at any given level in water are given. Then, the exact explicit expressions to the fourth order of mu are derived. Finally, the linear solutions of eta, (U) over right arrow, C (phase-celerity) and C-g (group velocity) for a constant water depth are obtained. Compared with the Airy theory, excellent results can be found even for a water depth as large as the wave legnth. The present high-order models are applicable to nonlinear regular and irregular waves in water of any varying depth (from shallow to deep) and bottom slope (from mild to steep).
基金＊Supported by the National Natural Science Foundation of China under Grant No. 40876010, the Main Direction Program of the Knowledge Innovation Project of Chinese Academy of Sciences under Grant No. KZCX2-YW-Q03-08, the R ＆： D Special Fund for Public Welfare Industry （Meteorology） under Grant No. GYHY200806010, the LASG State Key Laboratory Special Fund and the Foundation of E-Institutes of Shanghai Municipal Education Commission （E03004）
文摘The approximate expressions of the travelling wave solutions for a class of nonlinear disturbed long-wave system are constructed using the generalized variational iteration method.
基金the National Natural Science Foundation of China (Grant No.40234043)
文摘From April, 2003 to September, 2004, a passive broadband seismic array consisting of 60 stations was deployed over the Tianshan orogenic belt by State Key Laboratory of Earthquake Dynamics, Institute of Geology, China Earthquake Administration. Among them, 51 stations make up an about 500-km-long profile across the Tianshan Mountains from Kuytun to Kuqa. The receiver function profile and S-wave velocity structure of the crust and upper mantle down to 100 km deep are obtained by using the re-ceiver function method (Liu et al. 1996, 2000). The main results can be summarized as follows: (1) A clear mountain root does not exist beneath the Tianshan Mountains, and the crust-mantle boundaries underneath the stations mostly have transitional structures. This implies that the material differentia-tion between the crust and mantle is not yet accomplished and the orogenic process is still going on. (2) The crust beneath the Tianshan Mountains has laterally blocked structures in direction perpendicular to the mountain strike, and the crust-mantle boundary has a clear dislocation structure. Both of them correspond to each other. (3) The offsets of the Moho discontinuity are highly correlated to the tectonic borders on the surface and that corresponding to the frontal southern Tianshan fault reaches to 14 km. This manifests that large vertical divergent movement took place between different blocks. This sup-ports the discontinuous model of the Tianshan orogeny, and the Tarim block subduction is restricted only to the southern side of the South Tianshan. (4) Inside the upper and middle crust of the Tianshan Mountains exist several low-velocity bodies correlated with high seismicity located on the moun-tain-basin jointures on both sides of the mountain and between different blocks, and the low-velocity bodies on the mountain-basin jointures are inclined obviously to the mountain. This implies that the low-velocity bodies may be correlated closely to the thrust and subduction of the basins on both sides of the mountain, the spli
文摘From the nonlinear sine-Gordon equation, new transformations are obtained in this paper, which are applied to propose a new approach to construct exact periodic solutions to nonlinear wave equations. It is shown that more new periodic solutions can be obtained by this new approach, and more shock wave solutions or solitary wave solutions can be got under their limit conditions.
文摘The elliptic equation is taken as a transformation and applied to solve nonlinear wave equations. It is shown that this method is more powerful to give more kinds of solutions, such as rational solutions, solitary wave solutions,periodic wave solutions and so on, so it can be taken as a generalized method.
