Backlund transformation, exact solutions and diverse interaction phenomena to a (3+1)-dimensional nonlinear evolution equation

Under investigation in this paper is a (3+1)-dimensional nonlinear evolution equation, which was proposed and analyzed to study features and properties of nonlinear dynamics in higher dimensions. Using the Hirota bilinear method, we construct a bilinear Backlund transformation, which consists of four equations and involves six free parameters. With test function method and symbolic computation, three sets of lump-kink solutions and new types of interaction solutions are derived, and figures are presented to reveal the interaction behaviors. Setting constraints to the new interaction solution via the test function expressed by polynomial-cos-cosh, we simulate the periodic interaction phenomenon. Pfaffian solutions to the (3+1)-dimensional nonlinear evolution equation are obtained based on a set of linear partial differential conditions. According to our results, the diversity of solutions to the (3+1)-dimensional nonlinear evolution equation is revealed.

Automated summary

The paper investigates a (3+1)-dimensional nonlinear evolution equation to study features and properties of nonlinear dynamics in higher dimensions. By using the Hirota bilinear method, a bilinear Backlund transformation with six free parameters is constructed, resulting in multiple sets of solutions and new types of interaction solutions. The periodic interaction phenomenon is simulated by setting constraints to the new interaction solution expressed by polynomial-cos-cosh test function.