Spatiotemporal deformation of multi-soliton to (2 + 1)-dimensional KdV equation.

This work proposes a three-wave method with a perturbation parameter to obtain exact multi-soliton solutions of nonlinear evolution equation. The ( $$2+1$$ )-dimensional KdV equation is used as an example to illustrate the effectiveness of the suggested method. Using this method, new multi-soliton solutions are given. Specially, spatiotemporal dynamics of breather two-soliton and multi-soliton including deformation between bright and dark multi-soliton each other, and deflection with different directions and angles are investigated and exhibited to ( $$2+1$$ )D KdV equation. Some new nonlinear phenomena are revealed under the small perturbation of parameter. [ABSTRACT FROM AUTHOR]