Extreme coastal events require careful prediction of wave forces. Recent tsunamis have resulted in extensive damage of coastal structures. Such scenarios are the result of the action of long waves on structures. In th...Extreme coastal events require careful prediction of wave forces. Recent tsunamis have resulted in extensive damage of coastal structures. Such scenarios are the result of the action of long waves on structures. In this paper, the efficiency of vegetation as a buffer system in attenuating the incident ocean waves was studied through a well controlled experimental program. The study focused on the measurement of forces resulting from cnoidal waves on a model building mounted over a slope in the presence and absence of vegetation. The vegetative parameters, along with the width of the green belt, its position from the reference line, the diameter of the individual stems as well as the spacing between them, and their rigidity are varied so as to obtain a holistic view of the wave-vegetation interaction problem. The effect of vegetation on variations of dimensional forces with a Keulegan-Carpenter number (KC) was discussed in this paper. It has been shown that when vegetal patches are present in front of structure, the forces could be limited to within F*≤I, by a percentile of 92%, 90%, 55%, and 96%, respectively for gap ratios of 0.0, 0.5, 1.0, and 1.5. The force is at its maximum for the gap ratio of 1.0 and beyond which the forces start to diminish.展开更多
The nonlocal symmetry of the Boussinesq equation is obtained from the known Lax pair. The explicit analytic interaction solutions between solitary waves and cnoidal waves are obtained through the localization procedur...The nonlocal symmetry of the Boussinesq equation is obtained from the known Lax pair. The explicit analytic interaction solutions between solitary waves and cnoidal waves are obtained through the localization procedure of nonlocal symmetry. Some other types of solutions, such as rational solutions and error function solutions, are given by using the fourth Painlev~ equation with special values of the parameters. For some interesting solutions, the figures are given out to show their properties.展开更多
In this paper, the truncated Painleve analysis and the consistent tanh expansion (CTE) method are developed for the (2+1)-dimensional breaking soliton equation. As a result, the soliton-cnoidal wave interaction s...In this paper, the truncated Painleve analysis and the consistent tanh expansion (CTE) method are developed for the (2+1)-dimensional breaking soliton equation. As a result, the soliton-cnoidal wave interaction solution of the equation is explicitly given, which is dimcult to be found by other traditional methods. When the value of the Jacobi elliptic function modulus rn = 1, the soliton-cnoidal wave interaction solution reduces back to the two-soliton solution. The method can also be extended to other types of nonlinear evolution equations in mathematical physics.展开更多
Whitham–Broer–Kaup(WBK) equations in the shallow water small-amplitude regime is hereby under investigation. Nonlocal symmetry and Bcklund transformation are presented via the truncated Painlevé expansion.This ...Whitham–Broer–Kaup(WBK) equations in the shallow water small-amplitude regime is hereby under investigation. Nonlocal symmetry and Bcklund transformation are presented via the truncated Painlevé expansion.This residual symmetry is localised to Lie point symmetry by the properly enlarged system. The finite symmetry transformation of the prolonged system is computed. Based on the CTE method, WBK equations are linearized and new analytic interaction solutions between solitary waves and cnoidal waves are given with the aid of solutions for the linear equation.展开更多
A generalized Kadomtsev–Petviashvili equation is studied by nonlocal symmetry method and consistent Riccati expansion(CRE) method in this paper. Applying the truncated Painlevé analysis to the generalized Kadomt...A generalized Kadomtsev–Petviashvili equation is studied by nonlocal symmetry method and consistent Riccati expansion(CRE) method in this paper. Applying the truncated Painlevé analysis to the generalized Kadomtsev–Petviashvili equation, some B¨acklund transformations(BTs) including auto-BT and non-auto-BT are obtained. The auto-BT leads to a nonlocal symmetry which corresponds to the residual of the truncated Painlevé expansion. Then the nonlocal symmetry is localized to the corresponding nonlocal group by introducing two new variables. Further,by applying the Lie point symmetry method to the prolonged system, a new type of finite symmetry transformation is derived. In addition, the generalized Kadomtsev–Petviashvili equation is proved consistent Riccati expansion(CRE)solvable. As a result, the soliton-cnoidal wave interaction solutions of the equation are explicitly given, which are difficult to be found by other traditional methods. Moreover, figures are given out to show the properties of the explicit analytic interaction solutions.展开更多
文摘Extreme coastal events require careful prediction of wave forces. Recent tsunamis have resulted in extensive damage of coastal structures. Such scenarios are the result of the action of long waves on structures. In this paper, the efficiency of vegetation as a buffer system in attenuating the incident ocean waves was studied through a well controlled experimental program. The study focused on the measurement of forces resulting from cnoidal waves on a model building mounted over a slope in the presence and absence of vegetation. The vegetative parameters, along with the width of the green belt, its position from the reference line, the diameter of the individual stems as well as the spacing between them, and their rigidity are varied so as to obtain a holistic view of the wave-vegetation interaction problem. The effect of vegetation on variations of dimensional forces with a Keulegan-Carpenter number (KC) was discussed in this paper. It has been shown that when vegetal patches are present in front of structure, the forces could be limited to within F*≤I, by a percentile of 92%, 90%, 55%, and 96%, respectively for gap ratios of 0.0, 0.5, 1.0, and 1.5. The force is at its maximum for the gap ratio of 1.0 and beyond which the forces start to diminish.
基金supported by the National Natural Science Foundation of China(Nos.11275072,11435005)the Research Fund for the Doctoral Program of Higher Education of China(No.20120076110024)+3 种基金the Innovative Research Team Program of the National Natural Science Foundation of China(No.61321064)the Shanghai Knowledge Service Platform for Trustworthy Internet of Things(No.ZF1213)the Shanghai Minhang District Talents of High Level Scientific Research Project and the Talent FundK.C.Wong Magna Fund in Ningbo University
文摘The nonlocal symmetry of the Boussinesq equation is obtained from the known Lax pair. The explicit analytic interaction solutions between solitary waves and cnoidal waves are obtained through the localization procedure of nonlocal symmetry. Some other types of solutions, such as rational solutions and error function solutions, are given by using the fourth Painlev~ equation with special values of the parameters. For some interesting solutions, the figures are given out to show their properties.
基金Supported by National Natural Science Foundation of China under Grant Nos.11271211,11275072,11435005K.C.Wong Magna Fund in Ningbo University
文摘In this paper, the truncated Painleve analysis and the consistent tanh expansion (CTE) method are developed for the (2+1)-dimensional breaking soliton equation. As a result, the soliton-cnoidal wave interaction solution of the equation is explicitly given, which is dimcult to be found by other traditional methods. When the value of the Jacobi elliptic function modulus rn = 1, the soliton-cnoidal wave interaction solution reduces back to the two-soliton solution. The method can also be extended to other types of nonlinear evolution equations in mathematical physics.
基金Supported by the Key Foundation of Anhui Education Bureau under Grant No.KJ2013A028the 211 Project of Anhhui University under Grant No.J18520104+2 种基金Scientific Training Project for University StudentsNational Natural Science Foundation of China under Grant Nos.11471015,11571016Natural Science Foundation of Anhui Province under Grant No.1408085MA02
文摘Whitham–Broer–Kaup(WBK) equations in the shallow water small-amplitude regime is hereby under investigation. Nonlocal symmetry and Bcklund transformation are presented via the truncated Painlevé expansion.This residual symmetry is localised to Lie point symmetry by the properly enlarged system. The finite symmetry transformation of the prolonged system is computed. Based on the CTE method, WBK equations are linearized and new analytic interaction solutions between solitary waves and cnoidal waves are given with the aid of solutions for the linear equation.
基金Supported by the Global Change Research Program of China under Grant No.2015CB953904National Natural Science Foundation of under Grant Nos.11275072 and 11435005+3 种基金Doctoral Program of Higher Education of China under Grant No.20120076110024the Network Information Physics Calculation of Basic Research Innovation Research Group of China under Grant No.61321064Shanghai Collaborative Innovation Center of Trustworthy Software for Internet of Things under Grant No.ZF1213Zhejiang Provincial Natural Science Foundation of China under Grant No.LY14A010005
文摘A generalized Kadomtsev–Petviashvili equation is studied by nonlocal symmetry method and consistent Riccati expansion(CRE) method in this paper. Applying the truncated Painlevé analysis to the generalized Kadomtsev–Petviashvili equation, some B¨acklund transformations(BTs) including auto-BT and non-auto-BT are obtained. The auto-BT leads to a nonlocal symmetry which corresponds to the residual of the truncated Painlevé expansion. Then the nonlocal symmetry is localized to the corresponding nonlocal group by introducing two new variables. Further,by applying the Lie point symmetry method to the prolonged system, a new type of finite symmetry transformation is derived. In addition, the generalized Kadomtsev–Petviashvili equation is proved consistent Riccati expansion(CRE)solvable. As a result, the soliton-cnoidal wave interaction solutions of the equation are explicitly given, which are difficult to be found by other traditional methods. Moreover, figures are given out to show the properties of the explicit analytic interaction solutions.