New lump solutions to a (3+1)-dimensional generalized Calogero–Bogoyavlenskii–Schiff equation

Integrable nonlocal PT-symmetric generalized so(3,R) -mKdV equations

“…This guarantees that the potential reductions in (27) are compatible with the zero curvature equation of the integrable system (11).…”

“…T is given as in (11). Moreover, the infinitely many symmetries and conservation laws for the integrable system (11) are reduced to infinitely many ones for the above nonlocal integrable equations in (31), under (27).…”

“…For integrable equations associated with the special orthogonal Lie algebra ( ) so 3,  , there are still many interesting questions. Particularly, we would like to know how to formulate Riemann-Hilbert problems so that the associated inverse scattering transforms [11] could be presented and Nsoliton solutions [24,25] could be worked out, which might lead to lump wave solutions [26][27][28] or rogue wave solutions [29,30] to their higher-dimensional counterparts.…”

New lump solutions and several interaction solutions and their dynamics of a generalized (3+1)-dimensional nonlinear differential equation

“…then function f is positive definite. By symbolic computations, we obtain Therefore, according to theorem 2 in [36], the function f defined by equation (15) produces a lump solution of equation (1).…”

“…In [35], Ma first proposed a quadratic function method for constructing lump solutions of nonlinear differential equations, which can gain the lump solutions of high-dimensional nonlinear differential equations localized in the whole plane. Subsequently, Zhou et al derived the lump solutions of the (3+1)-dimensional generalized CBS equation and reduced the (3+1)-dimensional nonlinear evolution equation using a quadratic function method [36,37]. Inspired by the study of Ma et al, this paper aims to derive the lump solutions localized in the whole plane of a more generalized (3+1)-dimensional nonlinear differential equation…”