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Characteristics of solitary wave, homoclinic breather wave and rogue wave solutions in a (2+1)-dimensional generalized breaking soliton equation. (English) Zbl 1420.35301
Summary: 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.

MSC:
35Q51 Soliton equations
35C08 Soliton solutions
35Q53 KdV equations (Korteweg-de Vries equations)
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