(2+1)维Jaulent-Miodek方程的扭结孤子解

摘要

利用王明亮、李志斌和周宇斌提出的齐次平衡法研究了(2+1)维Jaulent-Miodek方程,得到该方程的四个新孤立波解.特别地,假设φ=1+eξ,在α=0,ξ0=0的情况下,得到该方程的两个扭结孤子解.更进一步,假设φ=1-eξ,在α=0,ξ0=0的情况下,得到该方程的两个奇异扭结孤子解.需要指出的是,在得到的扭结孤子解和奇异扭结孤子解中,有一个扭结孤子解和一个奇异扭结孤子解与马红彩、秦振云和邓爱平得出的解相一致.因此,本文除了得到四个新孤立波解以外,还得到一些新的扭结孤子解及奇异扭结孤子解.%In this paper,the homogeneous balance method proposed by Wang Mingliang,Li Zhibin and Zhou Yubin is adopted to study the (2 + 1)-dimensional Jaulent-Miodek equation,and four new solitary wave solutions of the equation are obtained.In particular,the two kink soliton solutions of the equation are obtained under the assumption that φ =1 + eξ in the case of oα =0,ξ0 =0.Furthermore,the two singular kink soliton solutions of the equation are also obtained under the assumption that φ =1-eξ in the case of α =0,ξ0 =0.It is pointed out that among the obtained kink soliton solutions and singular kink soliton solutions,there are a kink soliton solution and a singular kink soliton solution being consistent with the solution obtained by Ma Hongcai,Qin Zhenyun and Deng Aiping.Therefore,in addition to the four new solitary wave solutions,some new kink soliton solutions and singular kink soliton solutions are also obtained.