Soliton-like structures and the connection between the Bq and KP equations. (English) Zbl 1030.37051
Summary: We study the \((2+1)\)-dimensional model proposed by Kadomtsev and Petviashvili (KP) to describe slowly varying nonlinear waves in a dispersive medium. Applying an appropriate Lie transformation and following the method introduced by Tajiri et al., the KP equation is reduced to a one-dimensional equation, that is, to a certain version of the Boussinesq equation (BqE). Then, we solve the BqE by the Hirota method, and finally we use the inverse transformation in order to obtain de KP solutions. We analyze some remarkable properties of the solutions found in this work.
MSC:
| 37K40 | Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems |
| 35Q51 | Soliton equations |
| 35Q53 | KdV equations (Korteweg-de Vries equations) |
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