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Soliton-like structures and the connection between the Bq and KP equations

✍ Scribed by J. Bernal; Maximo A. Agüero; Erick Flores-Romero

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
948 KB
Volume
17
Category
Article
ISSN
0960-0779

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✦ Synopsis

We study the (2 þ 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.

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