In this paper, we use phase plane analysis to study the compactons of the nonlinear equation. Four new implicit expressions of the compactons are obtained. These new implicit expressions are given by inverse tangent f...In this paper, we use phase plane analysis to study the compactons of the nonlinear equation. Four new implicit expressions of the compactons are obtained. These new implicit expressions are given by inverse tangent functions. Our work extends previous results. For two sets of the data, the graphs of the implicit functions are drawn and numerical simulations are given to test the correctness of our theoretical results.展开更多
Recently,many authors have studied the following CH-γequation:ut+c0ux+3uux-α2(wxxt+uuxxx+2uxuxx)4-γuxxx=0,whereα2,c0 andγare paramters.Its bounded wave solutions have been investigated mainly for the caseα2>0...Recently,many authors have studied the following CH-γequation:ut+c0ux+3uux-α2(wxxt+uuxxx+2uxuxx)4-γuxxx=0,whereα2,c0 andγare paramters.Its bounded wave solutions have been investigated mainly for the caseα2>0.For the caseα2<0,the existence of three bounded waves(regular solitary waves,compactons,periodic peakons)was pointed out by Dullin et al.But the proof has not been given.In this paper,not only the existence of four types of bounded waves:periodic waves,compacton-like waves,kink-like waves,regular solitary waves,is shown,but also their explicit expressions or implicit expressions are given for the caseα2<0.Some planar graphs of the bounded wave solutions and their numerical simulations are given to show the correctness of our results.展开更多
基金Supported by the National Natural Science Foundation of China （No.10571062 10371037）.Acknowledgment The first author thanks to the Department of Science and Technology of Yuxi City for its support for doing this work.
文摘In this paper, we use phase plane analysis to study the compactons of the nonlinear equation. Four new implicit expressions of the compactons are obtained. These new implicit expressions are given by inverse tangent functions. Our work extends previous results. For two sets of the data, the graphs of the implicit functions are drawn and numerical simulations are given to test the correctness of our theoretical results.
基金This work was supported by the National Natural Science Foundation of China(Grant No.10571062)
文摘Recently,many authors have studied the following CH-γequation:ut+c0ux+3uux-α2(wxxt+uuxxx+2uxuxx)4-γuxxx=0,whereα2,c0 andγare paramters.Its bounded wave solutions have been investigated mainly for the caseα2>0.For the caseα2<0,the existence of three bounded waves(regular solitary waves,compactons,periodic peakons)was pointed out by Dullin et al.But the proof has not been given.In this paper,not only the existence of four types of bounded waves:periodic waves,compacton-like waves,kink-like waves,regular solitary waves,is shown,but also their explicit expressions or implicit expressions are given for the caseα2<0.Some planar graphs of the bounded wave solutions and their numerical simulations are given to show the correctness of our results.
