Nonsingular rational solutions to integrable models (Q2658241)

The paper is devoted to generate lump solutions of the following equations: (1) The KP equation: \[\left(u_{t}+6 u u_{x}+u_{x x x}\right)_{x}+\alpha u_{y y}=0, \] (2) The DJKM equation:\[ w_{x x x x y}+2 w_{x x x} w_{y}+4 w_{x x y} w_{x}+6 w_{x y} w_{x x}-w_{y y y}-2 w_{x x t}=0, \] (3) The elliptic Toda equation: \[ \left(\frac{\partial^{2}}{\partial x^{2}}+\frac{\partial^{2}}{\partial y^{2}}\right)\left(\log u_{n}\right)=u_{n+1}-2 u_{n}+u_{n-1}, \] (4) The BKP equation: \[ \left(u_{t}+15 u u_{3 x}+15 u_{x}^{3}-15 u_{x} \mid u_{y}+u_{5 x}\right)_{x}+5 u_{3 x, y}-5 u_{y y}=0, \] (5) The Novikov-Veselov equation \[ 2 u_{t}+u_{x x x}+u_{y y y}+3\left(u \partial_{y}^{-1} u_{x}\right)_{x}+3\left(u \partial_{x}^{-1} u_{y}\right)_{y}=0, \] (6) The negative flow of BKP equation: \[ u_{y t}-u_{x x x y}-3\left(u_{x} u_{y}\right)_{x}+3 u_{x x}=0. \] To find lump solutions the authors develop a technique via Bäcklund transformations and nonlinear superposition formulae in the framework of Hirota's bilinear formalism. For the entire collection see [Zbl 1459.00016].