Lump and Interaction Solutions of Linear PDEs in (3 + 1)-Dimensions

Abstract

Linear partial differential equations in (3 + 1)-dimensions consisting of all mixed second-order derivatives are considered, and Maple symbolic computations are made to construct their lump and interaction solutions, including lump-periodic, lumpkink and lump-soliton solutions.

Soliton Molecules and Some Novel Types of Hybrid Solutions to (2 + 1)-Dimensional Variable-Coefficient Caudrey-Dodd-Gibbon-Kotera-Sawada Equation

“…Among these rational solutions, lump solutions, breather wave solutions, and rogue wave solutions are hot point all the time. Recently, the hybrid solutions of lump solutions with other types of solutions draw a lot of attention, which include lump-soliton [17][18][19], lump-kink solution [20], resonance stripe solitons [21][22][23], and some hybrid solutions [24][25][26]. Very recently, Lou [27] introduced a new possible mechanism, the velocity resonant, to form soliton molecules and asymmetric solitons of three (1 + 1)-dimensional fluid models: fifth-order KdV, SK equation, and KK equation.…”

The construction of solutions to Zakharov–Kuznetsov equation with fractional power nonlinear terms

“…For exact solutions of nonlinear differential equations, there are a large number of results (see, for example, Seadawy et al 's interesting works [24][25][26][27][28][29][30][31][32][33]). Recently, Ma et al proposed a powerful method, namely the transformed rational function method, for generating traveling wave solutions and studied deeply and extensively another kind of exact solutions called lump solutions [34][35][36][37][38][39][40][41].…”

Dynamics of Lump Solutions, Rogue Wave Solutions and Traveling Wave Solutions for a (3 + 1)-Dimensional VC-BKP Equation

“…In past decades such equations have been studied by mathematicians and physicists. The NLEEs demonstrate both inelastic interactions and admit localised coherent structures [5,20,40,43]. The nonlinear B-type Kadomtsev-Petviashvili (KP) equation is an important representative of such equations -cf.…”