Lump solutions to a generalized Hietarinta-type equation via symbolic computation. (English) Zbl 1442.35366
Summary: Lump solutions are one of important solutions to partial differential equations, both linear and nonlinear. This paper aims to show that a Hietarinta-type fourth-order nonlinear term can create lump solutions with second-order linear dispersive terms. The key is a Hirota bilinear form. Lump solutions are constructed via symbolic computations with Maple, and specific reductions of the resulting lump solutions are made. Two illustrative examples of the generalized Hietarinta-type nonlinear equations and their lumps are presented, together with three-dimensional plots and density plots of the lump solutions.
MSC:
| 35Q51 | Soliton equations |
| 35Q53 | KdV equations (Korteweg-de Vries equations) |
| 37K40 | Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems |
| 68W30 | Symbolic computation and algebraic computation |
Keywords:
soliton equation; lump solution; symbolic computation; Hirota derivative; dispersion relationSoftware:
MapleReferences:
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