We show existence of global solutions for the gravity water waves equation in dimension 3, in the case of small data. The proof combines energy estimates, which yield control of L related norms, with dispersive estimates, which give decay in L∞. To obtain these dispersive estimates, we use an analysis in Fourier space; the study of space and time resonances is then the crucial point.

This paper provides an investigation on nonlinear dynamic behaviors of the (3+1)-dimensional B-type Kadomtsev—Petviashvili equation, which is used to model propagation weakly dispersive waves in a fluid. With help Cole—Hopf transform, Hirota bilinear equation established, then symbolic computation with ansatz function schemes employed search for diverse exact solutions. Some new results such as...

In this article, (3+1)-dimensional generalized Shallow Water-like (gSWl) equation is discussed. The infinitesimal generators of the are derived by using Lie symmetry analysis method. optimal system obtained based on adjoint table equation. Exact solutions constructed applying reduction, Exp <mml:mro...

Abstract In this article, through the Hirota bilinear method and long wave limit method, based on N-solitons, we construct multiple lump solutions of generalized (3+1)-dimensional Hirota–Satsuma–Ito equation. Furthermore, to enhance our understanding obtained, further elucidate physical implications these with three-dimensional two-dimensional graphs. The obtained might have practical applicati...