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 secon...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.展开更多
基金This work was supported in part by the National Natural Science Foundation of China(Grant Nos.11975145,11972291)the National Science Foundation(DMS-1664561)the Natural Science Foundation for Colleges and Universities in Jiangsu Province(17KJB110020).
文摘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.
