A simple algebraic transformation relation of a special type of solution between the (3+1)-dimensionalKadomtsev-petviashvili (KP) equation and the cubic nonlinear Klein Gordon equation (NKG) is established. Us-ing kno...A simple algebraic transformation relation of a special type of solution between the (3+1)-dimensionalKadomtsev-petviashvili (KP) equation and the cubic nonlinear Klein Gordon equation (NKG) is established. Us-ing known solutions of the NKG equation, we can obtain many soliton solutions and periodic solution of the (3+1)-dimensional KP equation.展开更多
Various types of wave group solutions of the weakly nonlinear waves may exist over uneven bottoms. In this paper, the variation of the zeroes of the dispersive and nonlinear terms,and the wave group solution in the th...Various types of wave group solutions of the weakly nonlinear waves may exist over uneven bottoms. In this paper, the variation of the zeroes of the dispersive and nonlinear terms,and the wave group solution in the third-order evolution equations are described for the case of mild and locally fastvarying water depths.展开更多
The extended tanh method is further improved by generalizing the Riccati equation and introducing its twenty seven new solutions. As its application, the (2+ 1)-dimensional Broer-Kaup equation is investigated and then...The extended tanh method is further improved by generalizing the Riccati equation and introducing its twenty seven new solutions. As its application, the (2+ 1)-dimensional Broer-Kaup equation is investigated and then its fifty four non-travelling wave solutions have been obtained. The results reported in this paper show that this method is more powerful than those, such as tanh method, extended tanh method, modified extended tanh method and Riccati equation expansion method introduced in previous literatures.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.
With the use of computer algebra, the method that straightforwardly leads to travelling wave solutions is presented. The compound KdV-Burgers equation and KP-B equation are chosen to illustrate this approach. As a res...With the use of computer algebra, the method that straightforwardly leads to travelling wave solutions is presented. The compound KdV-Burgers equation and KP-B equation are chosen to illustrate this approach. As a result, their abundant new soliton-like solutions and period form solutions are found.展开更多
A unified approach is presented for finding the travelling wave solutions to one kind of nonlinear evolution equation by introducing a concept of 'rank'. The key idea of this method is to make use of the arbit...A unified approach is presented for finding the travelling wave solutions to one kind of nonlinear evolution equation by introducing a concept of 'rank'. The key idea of this method is to make use of the arbitrariness of the manifold in Painlevé analysis. We selected a new expansion variable and thus obtained a rich variety of travelling wave solutions to nonlinear evolution equation, which covered solitary wave solutions, periodic wave solutions, Weierstrass elliptic function solutions, and rational solutions. Three illustrative equations are investigated by this means, and abundant travelling wave solutions are obtained in a systematic way. In addition, some new solutions are firstly reported here.展开更多
Under the travelling wave transformation, some nonlinear partial differential equations such as Camassa-Holm equation, High-order KdV equation, etc., are reduced to an integrable ODE expressed by u＂ ＋p（u）（u＇）^2...Under the travelling wave transformation, some nonlinear partial differential equations such as Camassa-Holm equation, High-order KdV equation, etc., are reduced to an integrable ODE expressed by u＂ ＋p（u）（u＇）^2 ＋ q（u） = 0 whose generai solution can be given. Furthermore, combining complete discrimination system for polynomiai, the classifications of all single travelling wave solutions to these equations are obtained. The equation u＂＋p（u）（u＇）^2＋q（u） = 0 includes the equation （u＇）^2 = f（u） as a special case, so the proposed method can be also applied to a large number of nonlinear equations. These complete results cannot be obtained by any indirect method.展开更多
The numerical prediction of added resistance and vertical ship motions of one ITTC （Intemational Towing Tank Conference） S-175 containership in regular head waves by our own in-house unsteady RANS solver naoe-FOAM-S...The numerical prediction of added resistance and vertical ship motions of one ITTC （Intemational Towing Tank Conference） S-175 containership in regular head waves by our own in-house unsteady RANS solver naoe-FOAM-SJTU is presented in this paper. The development of the solver naoe-FOAM-SJTU is based on the open source CFD tool, OpenFOAM. Numerical analysis is focused on the added resistance and vertical ship motions （heave and pitch motions） with four very different wavelengths （ 0.8Lpp 〈 2 〈 1.5L ） in regular head waves. Once the wavelength is near the length of the ship model, the responses of the resistance and ship motions become strongly influenced by nonlinear factors, as a result difficulties within simulations occur. In the paper, a comparison of the experimental results and the nonlinear strip theory was reviewed and based on the findings, the RANS simulations by the solver naoe-FOAM-SJTU were considered competent with the prediction of added resistance and vertical ship motions in a wide range of wave lengths.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 exact chirped soliton-like and quasi-periodic wave solutions of （2 ＋ 1）-dimensional generalized nonlinear Schr6dinger equation including linear and nonlinear gain （loss） with variable coefficients are obtaine...The exact chirped soliton-like and quasi-periodic wave solutions of （2 ＋ 1）-dimensional generalized nonlinear Schr6dinger equation including linear and nonlinear gain （loss） with variable coefficients are obtained detalledly in this paper. The form and the behavior of solutions are strongly affected by the modulation of both the dispersion coefficient and the nonlinearity coefficient. In addition, self-similar soliton-like waves precisely piloted from our obtained solutions by tailoring the dispersion and linear gain （loss）.展开更多
In this paper, we discuss conditional stability of solitary-wave solutions in the sense of Liapunov for the generalized compound KdV equation and the generalized compound KdV-Burgers equations. Linear stability of the...In this paper, we discuss conditional stability of solitary-wave solutions in the sense of Liapunov for the generalized compound KdV equation and the generalized compound KdV-Burgers equations. Linear stability of the exact solitary-wave solutions is proved for the above two types of equations when the small disturbance of travelling wave form satisfies some special conditions.展开更多
In this paper, the approximate expressions of the solitary wave solutions for a class of nonlinear disturbed long-wave system are constructed using the homotopie mapping method.
Based on computerized symbolic computation,a new method and its algorithm are proposed for searching for exact travelling wave solutions of the nonlinear partial differential equations.Making use of our approach,we in...Based on computerized symbolic computation,a new method and its algorithm are proposed for searching for exact travelling wave solutions of the nonlinear partial differential equations.Making use of our approach,we investigate the Whitham-Broer-Kaup equation in shallow water and obtain new families of exact solutions,which include soliton-like solutions and periodic solutions.As its special cases,the solutions of classical long wave equations and modified Boussinesq equations can also be found.展开更多
A complete approximate symmetry classification of a class of perturbed nonlinear wave equations isperformed using the method originated from Fushchich and Shtelen.Moreover,large classes of approximate invariantsolutio...A complete approximate symmetry classification of a class of perturbed nonlinear wave equations isperformed using the method originated from Fushchich and Shtelen.Moreover,large classes of approximate invariantsolutions of the equations based on the Lie group method are constructed.展开更多
文摘A simple algebraic transformation relation of a special type of solution between the (3+1)-dimensionalKadomtsev-petviashvili (KP) equation and the cubic nonlinear Klein Gordon equation (NKG) is established. Us-ing known solutions of the NKG equation, we can obtain many soliton solutions and periodic solution of the (3+1)-dimensional KP equation.
文摘Various types of wave group solutions of the weakly nonlinear waves may exist over uneven bottoms. In this paper, the variation of the zeroes of the dispersive and nonlinear terms,and the wave group solution in the third-order evolution equations are described for the case of mild and locally fastvarying water depths.
文摘The extended tanh method is further improved by generalizing the Riccati equation and introducing its twenty seven new solutions. As its application, the (2+ 1)-dimensional Broer-Kaup equation is investigated and then its fifty four non-travelling wave solutions have been obtained. The results reported in this paper show that this method is more powerful than those, such as tanh method, extended tanh method, modified extended tanh method and Riccati equation expansion method introduced in previous literatures.
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 project supported by the National Key Basic Research Development Project Program under Grant No.G1998030600the Foundation of Liaoning Normal University
文摘With the use of computer algebra, the method that straightforwardly leads to travelling wave solutions is presented. The compound KdV-Burgers equation and KP-B equation are chosen to illustrate this approach. As a result, their abundant new soliton-like solutions and period form solutions are found.
文摘A unified approach is presented for finding the travelling wave solutions to one kind of nonlinear evolution equation by introducing a concept of 'rank'. The key idea of this method is to make use of the arbitrariness of the manifold in Painlevé analysis. We selected a new expansion variable and thus obtained a rich variety of travelling wave solutions to nonlinear evolution equation, which covered solitary wave solutions, periodic wave solutions, Weierstrass elliptic function solutions, and rational solutions. Three illustrative equations are investigated by this means, and abundant travelling wave solutions are obtained in a systematic way. In addition, some new solutions are firstly reported here.
文摘Under the travelling wave transformation, some nonlinear partial differential equations such as Camassa-Holm equation, High-order KdV equation, etc., are reduced to an integrable ODE expressed by u＂ ＋p（u）（u＇）^2 ＋ q（u） = 0 whose generai solution can be given. Furthermore, combining complete discrimination system for polynomiai, the classifications of all single travelling wave solutions to these equations are obtained. The equation u＂＋p（u）（u＇）^2＋q（u） = 0 includes the equation （u＇）^2 = f（u） as a special case, so the proposed method can be also applied to a large number of nonlinear equations. These complete results cannot be obtained by any indirect method.
基金Foundation item： Supported by the National Natural Science Foundation of China （Grant No. 50739004 and 11072154）
文摘The numerical prediction of added resistance and vertical ship motions of one ITTC （Intemational Towing Tank Conference） S-175 containership in regular head waves by our own in-house unsteady RANS solver naoe-FOAM-SJTU is presented in this paper. The development of the solver naoe-FOAM-SJTU is based on the open source CFD tool, OpenFOAM. Numerical analysis is focused on the added resistance and vertical ship motions （heave and pitch motions） with four very different wavelengths （ 0.8Lpp 〈 2 〈 1.5L ） in regular head waves. Once the wavelength is near the length of the ship model, the responses of the resistance and ship motions become strongly influenced by nonlinear factors, as a result difficulties within simulations occur. In the paper, a comparison of the experimental results and the nonlinear strip theory was reviewed and based on the findings, the RANS simulations by the solver naoe-FOAM-SJTU were considered competent with the prediction of added resistance and vertical ship motions in a wide range of wave lengths.
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.
基金Supported by the National Natural Science Foundation of China under Grant No.11072219the Zhejiang Provincial Natural Science Foundation under Grant No.Y1100099
文摘The exact chirped soliton-like and quasi-periodic wave solutions of （2 ＋ 1）-dimensional generalized nonlinear Schr6dinger equation including linear and nonlinear gain （loss） with variable coefficients are obtained detalledly in this paper. The form and the behavior of solutions are strongly affected by the modulation of both the dispersion coefficient and the nonlinearity coefficient. In addition, self-similar soliton-like waves precisely piloted from our obtained solutions by tailoring the dispersion and linear gain （loss）.
基金The project supported by National Natural Science Foundation of China under Grant No. 10371023 and Shanghai Leading Academic Discipline Project under Grant No. T0502）
文摘In this paper, we discuss conditional stability of solitary-wave solutions in the sense of Liapunov for the generalized compound KdV equation and the generalized compound KdV-Burgers equations. Linear stability of the exact solitary-wave solutions is proved for the above two types of equations when the small disturbance of travelling wave form satisfies some special conditions.
基金Supported by the National Natural Science Foundation of China under Grant No.40876010the Main Direction Program of the Knowledge Innovation Project of Chinese Academy of Sciences under Grant No.KZCX2-YW-Q03-08+2 种基金the LASG State Key Laboratory Special Fundthe Foundation of Shanghai Municipal Education Commission under Grant No.E03004the Natural Science Foundation of Zhejiang Province under Grant No.Y6090164
文摘In this paper, the approximate expressions of the solitary wave solutions for a class of nonlinear disturbed long-wave system are constructed using the homotopie mapping method.
文摘Based on computerized symbolic computation,a new method and its algorithm are proposed for searching for exact travelling wave solutions of the nonlinear partial differential equations.Making use of our approach,we investigate the Whitham-Broer-Kaup equation in shallow water and obtain new families of exact solutions,which include soliton-like solutions and periodic solutions.As its special cases,the solutions of classical long wave equations and modified Boussinesq equations can also be found.
文摘A complete approximate symmetry classification of a class of perturbed nonlinear wave equations isperformed using the method originated from Fushchich and Shtelen.Moreover,large classes of approximate invariantsolutions of the equations based on the Lie group method are constructed.
