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 ($$2+1$$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 ($$2+1$$2+1)D KdV equation. Some new nonlinear phenomena are revealed under the small perturbation of parameter.

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