In this paper, we apply the tanh-coth method and traveling wave transformation method for solving Gardner equations, including (1 + 1)-Gardner and (2 + 1)- Gardner equations. The tanh-coth method proved to be reliable...In this paper, we apply the tanh-coth method and traveling wave transformation method for solving Gardner equations, including (1 + 1)-Gardner and (2 + 1)- Gardner equations. The tanh-coth method proved to be reliable and effective in handling a large number of nonlinear dispersive and disperse equations. Through tanh-coth method, we get analytical expressions of soliton solutions of Gardner equations. The one-soliton solution is characterized by an infinite wing or infinite tail.展开更多
In this paper,two different methods for calculating the conservation laws are used,these are the direct construction of conservation laws and the conservation theorem proposed by Ibragimov.Using these two methods,we o...In this paper,two different methods for calculating the conservation laws are used,these are the direct construction of conservation laws and the conservation theorem proposed by Ibragimov.Using these two methods,we obtain the conservation laws of the Gardner equation,Landau-Ginzburg-Higgs equation and Hirota-Satsuma equation,respectively.展开更多
We construct the Darboux transformations, exact solutions, and infinite number of conservation laws for a semidiscrete Gardner equation. A special class of solutions of the semidiscrete equation, called table-top soli...We construct the Darboux transformations, exact solutions, and infinite number of conservation laws for a semidiscrete Gardner equation. A special class of solutions of the semidiscrete equation, called table-top solitons, are given. The dynamical properties of these solutions are also discussed.展开更多
文摘In this paper, we apply the tanh-coth method and traveling wave transformation method for solving Gardner equations, including (1 + 1)-Gardner and (2 + 1)- Gardner equations. The tanh-coth method proved to be reliable and effective in handling a large number of nonlinear dispersive and disperse equations. Through tanh-coth method, we get analytical expressions of soliton solutions of Gardner equations. The one-soliton solution is characterized by an infinite wing or infinite tail.
基金funded by the National Natural Science Foundation of China(Grant Nos.12371256&11971475)。
文摘In this paper,two different methods for calculating the conservation laws are used,these are the direct construction of conservation laws and the conservation theorem proposed by Ibragimov.Using these two methods,we obtain the conservation laws of the Gardner equation,Landau-Ginzburg-Higgs equation and Hirota-Satsuma equation,respectively.
文摘We construct the Darboux transformations, exact solutions, and infinite number of conservation laws for a semidiscrete Gardner equation. A special class of solutions of the semidiscrete equation, called table-top solitons, are given. The dynamical properties of these solutions are also discussed.
