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We consider a (2+1)-dimensional generalized breaking soliton (gBS) equation, which describes the interaction of the Riemann wave propagated along the y -axis with a long wave propagated along the x -axis. By using Bell’s polynomials, we derive a bilinear form of the gBS equation. Based on the resulting Hirota’s bilinear equation, we explicitly construct its soliton solutions. Furthermore, by using the extended homoclinic test theory, its homoclinic breather waves and rogue waves are well derived, respectively. It is hoped that our results can enrich the dynamical behavior of the gBS-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]

In this paper, the ( 3 + 1 ) -dimensional Hirota bilinear equation is investigated, which can be used to describe the nonlinear dynamic behavior in physics. By using the Bell polynomials, the bilinear form of the equation is derived in a very natural way. Based on the resulting bilinear form, its N -solitary waves are further obtained by using the Hirota’s bilinear theory. Finally, by using the Homoclinic test method, we obtain its rational breather wave and rogue wave solutions, respectively. In order to better understand the dynamical behaviors of the equation, some graphical analyses are discussed for these exact solutions. [ABSTRACT FROM AUTHOR]