In this paper, for the (3+1)-dimensional extended Jimbo–Miwa equation, by the direct algebraic method, together with the inheritance solving strategy, we construct its interaction solutions among solitons, rational waves, and periodic waves. Meanwhile, we construct its interaction solutions among solitons, breathers, and lumps of any higher orders by an [Formula: see text]-soliton decomposition algorithm, together with the parameters conjugated assignment and long-wave limit techniques. The highlight of the paper is that by applying new algorithms and new techniques, we obtained different types of new multiwave interaction solutions for the (3+1)-dimensional extended Jimbo–Miwa equation.

中文翻译：

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(3+1) 维扩展 Jimbo-Miwa 方程的多波相互作用解

本文针对(3+1)维扩展的Jimbo-Miwa方程，采用直接代数方法，结合继承求解策略，构造了孤子、有理波和周期波之间的相互作用解。同时，我们通过[公式：见正文]-孤子分解算法，结合参数共轭分配和长波极限技术，构造了孤子、呼吸子和任何高阶团块之间的相互作用解。论文的亮点在于，通过应用新算法和新技术，我们得到了(3+1)维扩展Jimbo-Miwa方程不同类型的新型多波相互作用解。