Quantum mechanics

Algorithm

Pure mathematics

Biology

Symbolic computation

Applied mathematics

Maple

Computation

Soliton

Computer science

Botany

Breather

Physics

Nonlinear system

Integrable system

Mathematics

Mathematical analysis

Artificial intelligence

Partial differential equation

Class (philosophy)

Modern Physics Letters B

The aim of this paper is to show that there exist lump solutions and interaction solutions to linear partial differential equations in 2[Formula: see text]+[Formula: see text]1 dimensions. Through symbolic computations with Maple, we exhibit a great variety of exact solutions to a class of (2[Formula: see text]+[Formula: see text]1)-dimensional linear partial differential equations, and present a specific example which possesses lump, lump-kink and lump-soliton solutions. This supplements the study on lump, rogue wave and breather solutions and their interaction solutions to nonlinear integrable equations.

Lump and interaction solutions to linear PDEs in 2+1 dimensions via symbolic computation