Abstract
Based on N-soliton solutions, fusion and fission waves are obtained through a new constraint among parameters. With this new constraint, fusion and fission phenomena can be reduced from N-soliton solutions in most (2+1)-dimensional integrable systems. This paper takes the (2+1)-dimensional fifth-order KdV equation as an example to introduce how to use this constraint to generate these fusion and fission waves in detail. At the same time, by continuing to introduce constraints like velocity resonance, module resonance, and long-wave limit, we can generate all kinds of hybrid solutions for granted, such as a hybrid of fissionable waves and breather waves, and a nonlinear superposition between fissionable waves and higher-order lump waves.
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