k > 0 , c > 0 , Δ ≥ 0

k > 0 , c > 0 , Δ ≥ 0

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Four (2+1)-dimensional nonlinear evolution equations, generated by the Jaulent-Miodek hierarchy, are investigated by the bifurcation method of planar dynamical systems. The bifurcation regions in different subsets of the parameters space are obtained. According to the different phase portraits in different regions, we obtain kink (antikink) wave so...

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Citations

... Bifurcation Method to Analysis of Traveling Wave Solutions 305 Four (2+1)-dimensional nonlinear models generated by the Jaulent-Miodek hierarchy [1][2][3][4] are extended in [5], which are ...
... The system(1) is completely integrable evolution equations. There are many methods to be used in travel wave soutions of nonlinear evolution equations, such as the inverse scattering method, the Bäcklund transformation method, algebraic-geometric method, the Darboux transformation method, multiple exp-function method [6], the Hirota bilinear method [1-3, 5, 7-9] and dynamical systems method [4,[10][11][12]. The Hirota bilinear method is used to formally derive the multiple kink solutions and multiple singular kink solutions of the (2+1)-dimensional nonlinear models [1], and multiple soliton solutions for the system (1) [5]. ...
... The Hirota bilinear method is used to formally derive the multiple kink solutions and multiple singular kink solutions of the (2+1)-dimensional nonlinear models [1], and multiple soliton solutions for the system (1) [5]. By the bifurcation method of the dynamical systems, some new exact solutions of the (2+1)-dimensional nonlinear models are obtained in [4]. In this paper, we will study the third model given ...
... Multiple kink solutions, multiple singular kink solutions and multiple soliton solutions were formally derived [1] and the exact traveling wave solutions of (1.1) have been obtained [7] .To our knowledge the study for the exact traveling wave solutions of (1.4) in different subsets of 4-parameters space of the system (1.7), has not been considered yet. By using the method of the dynamical systems, we shall generally investigate wave solutions of (1.4) in this paper. ...
... , using the information of the phase portraits in [7] , we analyze all the possible travel wave solutions of the system (1.4), which correspond to periodic travel wave solutions of the system (1.1). Some explicit parametric representations of traveling wave solutions of (1.4) are obtained. ...
... where α is constant [1] . The traveling wave system of (1.1) is derived [5] . Wazwaz [1] has obtained by Hirota bilinear method multiple soliton solutions which were formally derived. ...
... Wazwaz [1] has obtained by Hirota bilinear method multiple soliton solutions which were formally derived. In this paper, we research the travel wave solutions of (1.1) by bifucation method of dynamical systems [3,5] . ...
... The traveling wave solutions of (1.1) corresponding to peridioc wave solutions and solitary wave solutions, have been found in [5] completely. In this paper, we will research other traveling wave solutions which closely related to kink wave solutions of (1.2). ...
... where α is constant [1] . The traveling wave system of (1.1) is derived [5] . Wazwaz [1] has obtained by Hirota bilinear method multiple soliton solutions which were formally derived. ...
... Wazwaz [1] has obtained by Hirota bilinear method multiple soliton solutions which were formally derived. In this paper, we research the travel wave solutions of (1.1) by bifucation method of dynamical systems [3,5] . ...
... .2) has a valley type solitary wave solution [5] 1 ...
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