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In this work, we investigate the (3+1)-dimensional generalized B-type Kadomtsev–Petviashvili (gBKP) equation in fluid dynamics, which plays an important role in depicting weakly dispersive waves propagated in a quasi-media and fluid mechanics. By employing Hirota's bilinear method, we derive the one- and two-soliton solutions of the equation. Moreover, we reduce those soliton solutions to the periodic line waves and exact breather waves by considering different parameters. A long wave limit is used to derive the rogue wave solutions. Based on the resulting bilinear representation, we introduce two types of special polynomial functions, which are employed to find the lump solutions and interaction solutions between lump and stripe soliton. It is hoped that our results can be used to enrich dynamic behaviours of the (3+1)-dimensional BKP-type equations. [ABSTRACT FROM AUTHOR]

In this paper, the generalized variable-coefficient forced Kadomtsev-Petviashvili (gvcfKP) equation is investigated, which can be used to characterize the water waves of long wavelength relating to nonlinear restoring forces. Using a dependent variable transformation and combining the Bell's polynomials, we accurately derive the bilinear expression for the gvcfKP equation. By virtue of bilinear expression, its solitary waves are computed in a very direct method. By using the Riemann theta function, we derive the quasiperiodic solutions for the equation under some limitation factors. Besides, an effective way can be used to calculate its homoclinic breather waves and rogue waves, respectively, by using an extended homoclinic test function. We hope that our results can help enrich the dynamical behavior of the nonlinear wave equations with variable-coefficient. [ABSTRACT FROM AUTHOR]

We study a (2 + 1)-dimensional generalized Kadomtsev-Petviashvili (gKP) equation, which characterizes the formation of patterns in liquid drops. By using Bell's polynomials, an effective way is employed to succinctly construct the bilinear form of the gKP equation. Based on the resulting bilinear equation, we derive its solitary waves, rogue waves and homoclinic breather waves, respectively. Our results can help enrich the dynamical behavior of the KP-type equations. [ABSTRACT FROM AUTHOR]