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In this work, we consider the generalized (3 + 1)-dimensional Boussinesq equation, which can describe the propagation of gravity wave on the surface of water. Based on the Bell polynomial theory, a powerful technique is employed to explicitly construct its bilinear formalism and two-soliton solutions, based on which the new rational solution is well-constructed. Moreover, the extended homoclinic test approach is presented to succinctly construct the breather wave and rogue wave solutions of the Boussinesq equation. Then the main characteristics of these solutions are graphically discussed. More importantly, they reveal that the extreme behavior of the breather wave can give rise to the rogue wave. [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]