Symbolic computation of lump solutions to a combined equation involving three types of nonlinear terms. (English) Zbl 1464.35289
Summary: This paper aims to compute lump solutions to a combined fourth-order equation involving three types of nonlinear terms in \((2+1)\)-dimensions via symbolic computations. The combined nonlinear equation contains all second-order linear terms and it possesses a Hirota bilinear form under two logarithmic transformations. Two classes of explicit lump solutions are determined, which are associated with two cases of the coefficients in the model equation. Two illustrative examples of the combined nonlinear equation are presented, along with lump solutions and their representative threedimensional plots, contour plots and density plots.
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; Hirota derivative; symbolic computation; dispersion relationReferences:
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