Darboux Transformation of Generalized Coupled KdV Soliton Equation and Its Odd-Soliton Solutions
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摘要: 借助谱问题的规范变换, 给出广义耦合KdV孤子方程的达布变换,利用达布变换来产生广义耦合KdV孤子方程的奇孤子解,并且用行列式的形式来表达广义耦合KdV孤子方程的奇孤子解.作为应用,广义耦合KdV孤子方程奇孤子解的前两个例子被给出.Abstract: Based on the resulting Lax pairs of generalized coupled KdV soliton equation, a new Darboux transformation with multi-parameters for generalized coupled KdV soliton equation is derived with the help of a gauge transformation of the spectral problem. By using Darboux transformation, the generalized odd-soliton solutions of ceneralized coupled KdV soliton equation are given and presented in determinant form. As an application, the first two cases are given.
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Key words:
- Darboux transformation /
- soliton equation /
- odd-soliton solution /
- gauge transformation
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[1] LI Xue-mei,GENG Xian-guo.Lax matrix and a generalized coupled KdV hierarchy[J].Phys A,2003,327:357-370. doi: 10.1016/S0378-4371(03)00260-7 [2] 刘萍,张荣.广义耦合KdV孤子方程的达布变换及其精确解[J].洛阳师范学院学报,2005,24(5):1-5. [3] Li Y S, Ma W X, Zhang J E.Darboux transformation of classical Boussinesq system and its new solutions[J].Phys Lett A,2000,275:60-66. doi: 10.1016/S0375-9601(00)00583-1 [4] Li Y S, Zhang J E.Darboux transformation of classical Boussinesq system and its multi-solition solutions[J].Phys Lett A,2001,284:253-258. doi: 10.1016/S0375-9601(01)00331-0 [5] FAN En-gui.Darboux transformation and soliton-like solutions for the Gerdjikov-Ivanov equation[J].Phys A:Math Gen,2000,33:6925-6933. doi: 10.1088/0305-4470/33/39/308 [6] 张金顺,李华夏.2+1维Levi孤子方程的Darboux变换[J].郑州大学学报(自然科学版),2001,33(3):13-17. [7] 刘萍.Broer-Kaup系统的达布变换及其孤子解[J].数学物理学报,2006,26A(7):999-1007. [8] LIU Ping,ZHANG Jin-hun.Darboux transformation of Broer-Kaup system and its odd-soliton solutions[J].西南师范大学学报(自然科学版),2006,31(5):31-36. [9] Geng X G, Tam H W.Darboux transformation and soliton solutions for generalized nonlinear Schrdinger equation[J].Phys Soc Jpn,1999,68(5):1508-1512. doi: 10.1143/JPSJ.68.1508
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