Backlund transformation, Wronskian solutions and interaction solutions to the (3+1)-dimensional generalized breaking soliton equation

We focus on the (3+1)-dimensional generalized breaking soliton (GBS) equation, which describes a Riemann wave propagating along three spatial dimensions. The Wronskian solutions are derived for the (3+1)-dimensional GBS equation based on the Plucker relation for determinants. The lump-soliton solutions are generated by virtue of the test function method. Through the Backlund transformation (BT), we obtain various solutions via specifically choosing different seed solutions, including the Wronskian solutions and the interaction solutions. The relation between the Wronskian solutions and interaction solutions is established based on BT. The study of the (3+1)-dimensional GBS equation provides theoretical guidance for solving equations and increases the diversity of exact solutions.

Automated summary

This article focuses on the (3+1)-dimensional generalized breaking soliton (GBS) equation, which describes a Riemann wave propagating along three spatial dimensions. The Wronskian solutions are derived for the (3+1)-dimensional GBS equation based on the Plucker relation for determinants. The lump-soliton solutions are generated by virtue of the test function method. Through the Backlund transformation (BT), various solutions are obtained by specifically choosing different seed solutions, including the Wronskian solutions and the interaction solutions. The relation between the Wronskian solutions and interaction solutions is established based on BT. The study of the (3+1)-dimensional GBS equation provides theoretical guidance for solving equations and increases the diversity of exact solutions.