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In this paper, an effective algorithm for constructing nonlinear evolution equations (NLEEs) has been proposed. Particularly, the existence of resonant multi-soliton solutions in the newly generated NLEEs is verified and demonstrated, and the accuracy of the extracted resonant multi-soliton solutions has been proved at the same time. Firstly, via the linear superposition principle along with reverse engineering two new NLEEs arising from the B-type Kadomtsev–Petviashvili (BKP) equation are established and investigated as well. The first new NLEE is constructed with three time derivative terms, and the second one is constructed with three space dissipative terms, respectively. Besides, the infinite resonant multi-soliton solutions are extracted which enjoy a variety of inelastic interactions due to the fact that they are constructed with variable parameters. Then, the reliable judgments to the multi-soliton solutions are carried out. Finally, the Painlevé test is applied to examine the new equations and none of them passed the test. It is important to highlight that the presented method and NLEEs could be extended to diversify the problem of physical nature.

An effective approach for constructing novel KP-like equations