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Abstract
In this work, we investigate the (3+1)-dimensional B-type Kadomtsev–Petviashvili–Boussinesq equation, which can be used to describe the processes of interaction of exponentially localized structures. The breathers, lumps, and rogue waves of this equation are studied in detail via the Hirota bilinear method. More specifically, the general breathers, line breathers, and many kinds of interaction solutions are constructed by selecting the appropriate parameters. Based on the long wave limit method, some lumps, rogue waves, and their interaction solutions are derived. The dynamical characteristics of these solutions are vividly demonstrated through some graphical analyzes in the different planes.
Highlights
1 Introduction It is well known that some special type of exact solutions [1,2,3,4,5,6,7], including soliton, lump, breather, and rogue wave of nonlinear evolution equations (NLEEs) depict many physical scenarios occurring in diverse areas of physics
Several effective methods have been established by mathematicians and physicists to obtain the exact solutions of NLEEs, for instance, Painlevé analysis [13], Hirota bilinear method [14,15,16,17,18], Darboux transformation (DT) [19, 20], and so on [21]
3 Conclusion and discussion To conclude, based on the Hirota bilinear forms (2.1) of the (3 + 1)-dimensional B-type Kadomtsev–Petviashvili–Boussinesq equation, the breather waves and interaction solutions are discussed by the complex conjugate method on soliton solutions (2.4)
Summary
It is well known that some special type of exact solutions [1,2,3,4,5,6,7], including soliton (it has ionic and stability properties), lump (localized in all directions in the space), breather (localized in one certain direction with periodic structure), and rogue wave (localized in both time and space) of nonlinear evolution equations (NLEEs) depict many physical scenarios occurring in diverse areas of physics. For N = 3 in Eq (2.4), the interaction solutions between one soliton and breather of Eq (1.2) can be displayed in three different planes by selecting the following suitable pa-. The interaction solutions between soliton and general breather of Eq (1.2) can be expressed as follows:. The interaction between line rogue wave and lump can be constructed in the (y, z) plane if we choose the following parameters: q1 = q2 = 2 + i, q3 = q4 = 1
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