In this paper, the （2＋ 1）-dimensional soliton equation is mainly being discussed. Based on the Hirota direct method, Wronskian technique and the Pfattlan properties, the N-soliton solution, Wronskian and Grammian s...In this paper, the （2＋ 1）-dimensional soliton equation is mainly being discussed. Based on the Hirota direct method, Wronskian technique and the Pfattlan properties, the N-soliton solution, Wronskian and Grammian solutions have been generated.展开更多
The Korteweg-de Vries equation with a forcing term is established by recent studies as a simple mathematicalmodel of describing the physics of a shallow layer of fluid subject to external forcing.In the present paper,...The Korteweg-de Vries equation with a forcing term is established by recent studies as a simple mathematicalmodel of describing the physics of a shallow layer of fluid subject to external forcing.In the present paper,we study theanalytic solutions to the KdV equation with forcing term by using Hirota's direct method.Several exact solutions aregiven as examples,from which one can see that the same type soliton solutions can be excited by different forced term.展开更多
An exact two-soliton solution of discrete mKdv equation is derived by using the Hirota direct approach. In addition, we plot the soliton solutions to discuss the properties of solitons. It is worth while noting that w...An exact two-soliton solution of discrete mKdv equation is derived by using the Hirota direct approach. In addition, we plot the soliton solutions to discuss the properties of solitons. It is worth while noting that we obtain the completely elastic interaction between the two solitons.展开更多
Abstract By applying the Lie group method, the （2＋l）-dimensional soliton equation is reduced to some （1＋1）-dimensional nonlinear equations. Based upon some new explicit solutions of the （2＋1）-dimensional brea...Abstract By applying the Lie group method, the （2＋l）-dimensional soliton equation is reduced to some （1＋1）-dimensional nonlinear equations. Based upon some new explicit solutions of the （2＋1）-dimensional breaking soliton equation are obtained.展开更多
By means of the generalized direct method,a relationship is constructed between the new solutions andthe old ones of the (3+1)-dimensional breaking soliton equation.Based on the relationship,a new solution is obtained...By means of the generalized direct method,a relationship is constructed between the new solutions andthe old ones of the (3+1)-dimensional breaking soliton equation.Based on the relationship,a new solution is obtainedby using a given solution of the equation.The symmetry is also obtained for the (3+1)-dimensional breaking solitonequation.By using the equivalent vector of the symmetry,we construct a seven-dimensional symmetry algebra and getthe optimal system of group-invariant solutions.To every case of the optimal system,the (3+1)-dimensional breakingsoliton equation is reduced and some solutions to the reduced equations are obtained.Furthermore,some new explicitsolutions are found for the (3+1)-dimensional breaking soliton equation.展开更多
Based on the general direct method developed by Lou et al. [J. Phys. A： Math. Gen. 38 （2005） L129], the symmetry group theorem is obtained, from that both the Lie point groups and the non-Lie symmetry groups of the...Based on the general direct method developed by Lou et al. [J. Phys. A： Math. Gen. 38 （2005） L129], the symmetry group theorem is obtained, from that both the Lie point groups and the non-Lie symmetry groups of the Konopelchenk-Dubrovsky （KD） equation are obtained. From the theorem, some exact solutions of KD equation are derived from a simple travelling wave solution and a multi-soliton solution.展开更多
Solitary rectal ulcer syndrome(SRUS) is a benign and chronic disorder well known in young adults and less in children.It is often related to prolonged excessive straining or abnormal defecation and clinically presents...Solitary rectal ulcer syndrome(SRUS) is a benign and chronic disorder well known in young adults and less in children.It is often related to prolonged excessive straining or abnormal defecation and clinically presents as rectal bleeding,copious mucus discharge,feeling of incomplete defecation,and rarely rectal prolapse.SRUS is diagnosed based on clinical symptoms and endoscopic and histological findings.The current treatments are suboptimal,and despite correct diagnosis,outcomes can be unsatisfactory.Some treatment protocols for SRUS include conservative management such as family reassurance,regulation of toilet habits,avoidance of straining,encouragement of a high-fiber diet,topical treatments with salicylate,sulfasalazine,steroids and sucralfate,and surgery.In children,SRUS is relatively uncommon but troublesome and easily misdiagnosed with other common diseases,however,it is being reported more than in the past.This condition in children is benign;however,morbidity is an important problem as reflected by persistence of symptoms,especially rectal bleeding.In this review,we discuss current diagnosis and treatment for SRUS.展开更多
Many observations show that in the Yellow Sea internal tidal waves (ITWs) possess the remarkable characteristics of internal Kelvin wave, and in the South Yellow Sea (SYS) the nonlinear evolution of internal tidal wav...Many observations show that in the Yellow Sea internal tidal waves (ITWs) possess the remarkable characteristics of internal Kelvin wave, and in the South Yellow Sea (SYS) the nonlinear evolution of internal tidal waves is one of the mechanisms producing internal solitary waves (ISWs), which is different from the generation mechanism in the case where the semidiurnal tidal current flows over topographic drops. In this paper, the model of internal Kelvin wave with continuous stratification is given, and an elementary numerical study of nonlinear evolution of ITWs is made for the SYS, using the generalized KdV model (GKdV model for short) for a continuous stratified ocean, in which the different effects of background barotropic ebb and flood currents are considered. Moreover, the parameterization of vertical turbulent mixing caused by ITWs and ISWs in the SYS is studied, using a parameterization scheme which was applied to numerical experiments on the breaking of ISWs by Vlasenko and Hutter in 2002. It is found that the vertical turbulent mixing caused by internal waves is very strong within the upper layer with depth less than about 30m, and the vertical turbulent mixing caused by ISWs is stronger than that by ITWs.展开更多
A special two-soliton solution of sine-Gordon equation is obtained by using the Hirota direct method. It is shown in a mass-centre system how two kinks move and interact with each other.
With the aid of binary Bell polynomial and a general Riemann theta function, we introduce how to obtain the exact periodic wave solutions by applying the generalized Dpˉ-operators in term of the Hirota direct method ...With the aid of binary Bell polynomial and a general Riemann theta function, we introduce how to obtain the exact periodic wave solutions by applying the generalized Dpˉ-operators in term of the Hirota direct method when the appropriate value of pˉ is determined. Furthermore, the resulting approach is applied to solve the extended(2+1)-dimensional Shallow Water Wave equation, and the periodic wave solution is obtained and reduced to soliton solution via asymptotic analysis.展开更多
基金Supported by the National Natural Science Foundation of China under Grant Nos.10771196 and 10831003the Natural Science Foundation of Zhejiang Province under Grant Nos.Y7080198 and R6090109
文摘In this paper, the （2＋ 1）-dimensional soliton equation is mainly being discussed. Based on the Hirota direct method, Wronskian technique and the Pfattlan properties, the N-soliton solution, Wronskian and Grammian solutions have been generated.
基金Supported by the GUCAS President Grant,the National Natural Science Foundation of China under Grant No.10701076
文摘The Korteweg-de Vries equation with a forcing term is established by recent studies as a simple mathematicalmodel of describing the physics of a shallow layer of fluid subject to external forcing.In the present paper,we study theanalytic solutions to the KdV equation with forcing term by using Hirota's direct method.Several exact solutions aregiven as examples,from which one can see that the same type soliton solutions can be excited by different forced term.
文摘An exact two-soliton solution of discrete mKdv equation is derived by using the Hirota direct approach. In addition, we plot the soliton solutions to discuss the properties of solitons. It is worth while noting that we obtain the completely elastic interaction between the two solitons.
基金The project supported by the Natural Science Foundation of Shandong Province of China under Grant No. 2004zx16
文摘Abstract By applying the Lie group method, the （2＋l）-dimensional soliton equation is reduced to some （1＋1）-dimensional nonlinear equations. Based upon some new explicit solutions of the （2＋1）-dimensional breaking soliton equation are obtained.
基金National Natural Science Foundation of China under Grant No.10735030Shanghai Leading Academic Discipline Project under Grant No.B412+1 种基金Natural Science Foundations of Zhejiang Province of China under Grant No.Y604056the Doctoral Foundation of Ningbo City under Grant No.2005A61030
文摘By means of the generalized direct method,a relationship is constructed between the new solutions andthe old ones of the (3+1)-dimensional breaking soliton equation.Based on the relationship,a new solution is obtainedby using a given solution of the equation.The symmetry is also obtained for the (3+1)-dimensional breaking solitonequation.By using the equivalent vector of the symmetry,we construct a seven-dimensional symmetry algebra and getthe optimal system of group-invariant solutions.To every case of the optimal system,the (3+1)-dimensional breakingsoliton equation is reduced and some solutions to the reduced equations are obtained.Furthermore,some new explicitsolutions are found for the (3+1)-dimensional breaking soliton equation.
基金Supported by the National Natural Science Foundation of China under Grant Nos.10747141 and 10735030Zhejiang Provincial Natural Science Foundations of China under Grant No.605408+3 种基金Ningbo Natural Science Foundation under Grant Nos.2007A610049 and 2008A610017National Basic Research Program of China (973 Program 2007CB814800)Shanghai Leading Academic Discipline Project under Grant No.B412K.C.Wong Magna Fund in Ningbo University
文摘Based on the general direct method developed by Lou et al. [J. Phys. A： Math. Gen. 38 （2005） L129], the symmetry group theorem is obtained, from that both the Lie point groups and the non-Lie symmetry groups of the Konopelchenk-Dubrovsky （KD） equation are obtained. From the theorem, some exact solutions of KD equation are derived from a simple travelling wave solution and a multi-soliton solution.
文摘Solitary rectal ulcer syndrome(SRUS) is a benign and chronic disorder well known in young adults and less in children.It is often related to prolonged excessive straining or abnormal defecation and clinically presents as rectal bleeding,copious mucus discharge,feeling of incomplete defecation,and rarely rectal prolapse.SRUS is diagnosed based on clinical symptoms and endoscopic and histological findings.The current treatments are suboptimal,and despite correct diagnosis,outcomes can be unsatisfactory.Some treatment protocols for SRUS include conservative management such as family reassurance,regulation of toilet habits,avoidance of straining,encouragement of a high-fiber diet,topical treatments with salicylate,sulfasalazine,steroids and sucralfate,and surgery.In children,SRUS is relatively uncommon but troublesome and easily misdiagnosed with other common diseases,however,it is being reported more than in the past.This condition in children is benign;however,morbidity is an important problem as reflected by persistence of symptoms,especially rectal bleeding.In this review,we discuss current diagnosis and treatment for SRUS.
基金supported by the Key Program of the National Natural Science Foundation of China under contract No.41030855
文摘Many observations show that in the Yellow Sea internal tidal waves (ITWs) possess the remarkable characteristics of internal Kelvin wave, and in the South Yellow Sea (SYS) the nonlinear evolution of internal tidal waves is one of the mechanisms producing internal solitary waves (ISWs), which is different from the generation mechanism in the case where the semidiurnal tidal current flows over topographic drops. In this paper, the model of internal Kelvin wave with continuous stratification is given, and an elementary numerical study of nonlinear evolution of ITWs is made for the SYS, using the generalized KdV model (GKdV model for short) for a continuous stratified ocean, in which the different effects of background barotropic ebb and flood currents are considered. Moreover, the parameterization of vertical turbulent mixing caused by ITWs and ISWs in the SYS is studied, using a parameterization scheme which was applied to numerical experiments on the breaking of ISWs by Vlasenko and Hutter in 2002. It is found that the vertical turbulent mixing caused by internal waves is very strong within the upper layer with depth less than about 30m, and the vertical turbulent mixing caused by ISWs is stronger than that by ITWs.
文摘A special two-soliton solution of sine-Gordon equation is obtained by using the Hirota direct method. It is shown in a mass-centre system how two kinks move and interact with each other.
基金Supported by Shandong Provincial Key Laboratory of Marine Ecology and Environment&Disaster Prevention and Mitigation project under Grant No.2012010National Natural Science Foundation of China under Grant No.11271007+1 种基金Special Funds for Theoretical Physics of the National Natural Science Foundation of China under Grant No.11447205Shandong University of Science and Technology Research Fund under Grant No.2012KYTD105
文摘With the aid of binary Bell polynomial and a general Riemann theta function, we introduce how to obtain the exact periodic wave solutions by applying the generalized Dpˉ-operators in term of the Hirota direct method when the appropriate value of pˉ is determined. Furthermore, the resulting approach is applied to solve the extended(2+1)-dimensional Shallow Water Wave equation, and the periodic wave solution is obtained and reduced to soliton solution via asymptotic analysis.
