Quantum mechanics

Ecology

Mathematical physics

Heat transfer

Biology

Rayleigh number

Soliton

Natural convection

Classical mechanics

Ansatz

Type (biology)

Physics

Nonlinear system

Mathematics

Quantum electrodynamics

Boussinesq approximation (buoyancy)

Work (physics)

Mathematical analysis

Mechanics

Convection

Chinese Journal of Physics

In this work, we develop two new types of (1+1)-dimensional nonlocal Boussinesq equations to represent more situations in complex water waves. By applying ansatz method, we construct the explicit soliton solutions for the equations. We give the parameter constraints of the existence of soliton solutions, trivial solutions and complex singular solutions. Moreover, we also investigate the impacts of the system parameter α on the solitons.

Two new types of nonlocal Boussinesq equations in water waves: Bright and dark soliton solutions