In this paper, using the reductive perturbation method combined with the PLK method and two- parameter expansions, we treat the problem of head- on collision between two solitary waves described by the generalized Korteweg- de Vries equation (the gKdV equation) and obtain its second-order approximate solution. The results show that after the collision, the gKdV solitary waves preserve their profiles and during the collision, the maximum amplitute is the linear superposition of two maximum amplitudes of the impinging solitary waves.
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Yong, Z., Shiqiang, D. On head-on collison between two gKdV solitary waves in a stratified fluid. Acta Mech Sinica 7, 300–308 (1991). https://doi.org/10.1007/BF02486737
- gKdV solitary wave
- head-on collision
- reductive perturbation method
- PLK method