Head-on collision between two mKdV solitary waves in a two-layer fluid system. (English) Zbl 0758.76073
The head-on collision between two solitary waves described by the modified KdV equation (the mKdV equation, for short) is investigated by using the reductive perturbation method combined with the PLK method. These waves propagate at the interface of a two-fluid system, in which the density ratio of the two fluids equals the square of the depth ratio of the fluids. The second order perturbation solution is obtained. It is found that in the case of disregarding the nonuniform phase shift, the solitary waves preserve their original profiles after collision, whereas after considering the nonuniform phase shift, the wave profiles may deform after collision.
MSC:
| 76V05 | Reaction effects in flows |
| 76B55 | Internal waves for incompressible inviscid fluids |
| 35Q53 | KdV equations (Korteweg-de Vries equations) |
| 76B25 | Solitary waves for incompressible inviscid fluids |
Keywords:
reductive perturbation method; PLK method; second order perturbation solution; nonuniform phase shiftReferences:
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