Multiple rogue wave and solitary solutions for the generalized BK equation via Hirota bilinear and SIVP schemes arising in fluid mechanics. (English) Zbl 1451.76026
Summary: The multiple lump solutions method is employed for the purpose of obtaining multiple soliton solutions for the generalized Bogoyavlensky-Konopelchenko (BK) equation. The solutions obtained contain first-order, second-order, and third-order wave solutions. At the critical point, the second-order derivative and Hessian matrix for only one point is investigated, and the lump solution has one maximum value. He’s semi-inverse variational principle (SIVP) is also used for the generalized BK equation. Three major cases are studied, based on two different ansatzes using the SIVP. The physical phenomena of the multiple soliton solutions thus obtained are then analyzed and demonstrated in the figures below, using a selection of suitable parameter values. This method should prove extremely useful for further studies of attractive physical phenomena in the fields of heat transfer, fluid dynamics, etc.
MSC:
| 76B15 | Water waves, gravity waves; dispersion and scattering, nonlinear interaction |
| 35Q53 | KdV equations (Korteweg-de Vries equations) |
| 35C08 | Soliton solutions |
| 35Q51 | Soliton equations |
Keywords:
multiple rogue wave solutions; multiple soliton solutions; generalized Bogoyavlensky-Konopelchenko equation; semi-inverse variational principleReferences:
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