In this paper, by using the sine-cosine method, the extended tanh-method, and the rational hyperbolic functions method, we study a class of nonlinear equations which derived from a fourth order analogue of generalized...In this paper, by using the sine-cosine method, the extended tanh-method, and the rational hyperbolic functions method, we study a class of nonlinear equations which derived from a fourth order analogue of generalized Camassa-Holm equation. It is shown that this class gives compactons, solitary wave solutions, solitons, and periodic wave solutions. The change of the physical structure of the solutions is caused by variation of the exponents and the coefficients of the derivatives.展开更多
Starting from the known variable separation excitations of a(2 + 1)-dimensional generalized Ablowitz-Kaup-Newell-Segur system,rich coherent structures can be derived.The interactions among different types of solitary ...Starting from the known variable separation excitations of a(2 + 1)-dimensional generalized Ablowitz-Kaup-Newell-Segur system,rich coherent structures can be derived.The interactions among different types of solitary waves like peakons,dromions,and compactons are investigated and some novel features or interesting behaviors are revealed.The results show that the interactions for peakon-dromion,compacton-dromion,and peakon-compacton may be completely nonelastic or completely elastic.展开更多
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
In this paper, generalized KdV equations are investigated by using a mathematical technique based on the reduction of order for solving differential equations. The compactons, solitons, solitary patterns and periodic ...In this paper, generalized KdV equations are investigated by using a mathematical technique based on the reduction of order for solving differential equations. The compactons, solitons, solitary patterns and periodic solutions for the equations presented in this paper are obtained. For these generalized KdV equations, it is found that the change of the exponents of the wave function u and the coefficient a, positive or negative, leads to the different physical structures of the solutions.展开更多
After some reduction procedure made on the nonlinear evolution equation for nerve pulses, based on thermodynamic principles, new classic and non-classic traveling solutions have been obtained. We have studied this mod...After some reduction procedure made on the nonlinear evolution equation for nerve pulses, based on thermodynamic principles, new classic and non-classic traveling solutions have been obtained. We have studied this model for particular values in the parameter space, and obtained both the bell and compacton like solutions. These nonlinear traveling waves could be responsible for transmitting efficiently the necessary information along the axons. The non-classic structures named as compactons, due to their robust configuration, could be considered in some sense a more realistic type of nonlinear chargers of information. The last solutions do not have tails and as adiabatic waves could propagate along the nerve with constant velocity that could be equal, smaller or higher than the sound velocity.展开更多
文摘In this paper, by using the sine-cosine method, the extended tanh-method, and the rational hyperbolic functions method, we study a class of nonlinear equations which derived from a fourth order analogue of generalized Camassa-Holm equation. It is shown that this class gives compactons, solitary wave solutions, solitons, and periodic wave solutions. The change of the physical structure of the solutions is caused by variation of the exponents and the coefficients of the derivatives.
文摘Starting from the known variable separation excitations of a(2 + 1)-dimensional generalized Ablowitz-Kaup-Newell-Segur system,rich coherent structures can be derived.The interactions among different types of solitary waves like peakons,dromions,and compactons are investigated and some novel features or interesting behaviors are revealed.The results show that the interactions for peakon-dromion,compacton-dromion,and peakon-compacton may be completely nonelastic or completely elastic.
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.
文摘In this paper, generalized KdV equations are investigated by using a mathematical technique based on the reduction of order for solving differential equations. The compactons, solitons, solitary patterns and periodic solutions for the equations presented in this paper are obtained. For these generalized KdV equations, it is found that the change of the exponents of the wave function u and the coefficient a, positive or negative, leads to the different physical structures of the solutions.
文摘After some reduction procedure made on the nonlinear evolution equation for nerve pulses, based on thermodynamic principles, new classic and non-classic traveling solutions have been obtained. We have studied this model for particular values in the parameter space, and obtained both the bell and compacton like solutions. These nonlinear traveling waves could be responsible for transmitting efficiently the necessary information along the axons. The non-classic structures named as compactons, due to their robust configuration, could be considered in some sense a more realistic type of nonlinear chargers of information. The last solutions do not have tails and as adiabatic waves could propagate along the nerve with constant velocity that could be equal, smaller or higher than the sound velocity.
