In this letter we report a new type of multi-soliton solutions for the modified Korteweg–de Vries (mKdV) equation. These solutions contain functions of the trigonometric solitons and classical solitons simultaneously. A new bilinear form of the mKdV equation is introduced to derive these solutions. The obtained solutions display as solitons living on a periodic background, which are analyzed and illustrated.

中文翻译：

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修正的 Korteweg–de Vries 方程的新型解


在这封信中，我们报告了改进的 Korteweg-de Vries (mKdV) 方程的新型多孤子解。这些解同时包含三角孤子和经典孤子的函数。引入 mKdV 方程的新双线性形式来导出这些解。所获得的解显示为生活在周期性背景上的孤子，并对其进行了分析和说明。