Construction of Stationary Solitary Wave Solutions
1985 年 54 巻 5 号 p. 1701-1709
詳細
1985 年 54 巻 5 号 p. 1701-1709
A construction of stationary solitary wave solutions to nonlinear partial differential equations is presented. First, it is shown that one of fifty Painlevé-type ordinary differential equations intimately connects with one-soliton solutions which are stationary solitary wave ones of usual soliton equations. Secondly, if these solutions are named the “1st-class”, by extending the Painlevé-type equation, we can newly construct three kinds (sech2, sech and combined forms) of the “Nth-class” stationary solitary wave solutions through special potential functions expressed by elementary ones.
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