Journal
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK
Volume 72, Issue 2, Pages -Publisher
SPRINGER INT PUBL AG
DOI: 10.1007/s00033-021-01482-1
Keywords
Irrotational incompressible fluid; (2+1)-dimensional Boiti-Leon-Manna-Pempinelli equation; Hybrid solutions; Modified Pfaffian technique
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Funding
- National Natural Science Foundation of China [11772017]
- Fundamental Research Funds for the Central Universities [50100002016105010]
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In this paper, the Pfaffian technique is optimized and the Boiti-Leon-Manna-Pempinelli equation for an irrotational incompressible fluid is investigated, with higher-order hybrid solutions constructed. The characteristics of the breather and lump, as well as the limitations of the hybrid solutions, are presented.
Fluids, as a phase of matter including liquids, gases and plasmas, are seen to be common in nature, the study of which helps the design in the related industries. In this paper, we optimize the Pfaffian technique and investigated the Boiti-Leon-Manna-Pempinelli equation for an irrotational incompressible fluid. Higher-order hybrid solutions consisting of the L lumps, M breathers and N solitons are constructed with L, M and N being positive integers. Relative extrema of the breather and lump are presented, respectively. Breather is found to be localized along the curve a(1)x+b(1)phi(y)+ omega(1)t + xi = 0 and periodic along the curve alpha(1)x + beta(1)phi(y) + gamma(1)t + theta(1) = 0. Under the lump existence condition, higher-order rogue wave solutions do not exist. Hybrid solutions composed of breathers, lumps and solitons are illustrated graphically. It can be found that when certain parameters are chosen, the breather, lump and soliton included in the hybrid solutions possess the same properties as those of the breather and lump solutions.
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