Smooth positon solutions of the focusing modified Korteweg–de Vries equation
Smooth positon solutions of the focusing modified Korteweg–de Vries equation
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DOI：
10.1007/s11071-017-3579-x
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发表时间：
2017-05
影响因子：
5.6
通讯作者：
Qiuxia Xing;Zhiwei Wu;D. Mihalache;Jingsong He
中科院分区：
文献类型：
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作者：
Qiuxia Xing;Zhiwei Wu;D. Mihalache;Jingsong He
聚焦实数修正 Korteweg–de Vries (mKdV) 方程的折达布变换以行列式表示形式表示。使用这种表示，mKdV 方程的孤子解也可以用行列式表示，行列式的元素由相关 Lax 方程的特征值和相应的特征函数组成。聚焦 mKdV 方程的非奇异位置解是在特殊极限下，从相应的 n 孤子解并使用相关的高阶泰勒展开式获得的。此外，还研究了当时位置解分解为单孤子解的方法、多位置的轨迹以及相应的“相移”。
Then-fold Darboux transformationof the focusing real modified Korteweg–de Vries (mKdV) equation is expressed in terms of the determinant representation. Using this representation, then-soliton solutions of the mKdV equation are also expressed by determinants whose elements consist of the eigenvaluesand the corresponding eigenfunctions of the associated Lax equation. The nonsingularn-positon solutions of the focusing mKdV equation are obtained in the special limit, from the correspondingn-soliton solutions and by using the associated higher-order Taylor expansion. Furthermore, the decomposition method of then-positon solution intonsingle-soliton solutions, the trajectories, and the corresponding “phase shifts” of the multi-positons are also investigated.