Some quasi-periodic solutions to the Kadometsev-Petviashvili and modified Kadometsev-Petviashvili equations
✍ Scribed by J. Chen; X. Geng
- Book ID
- 111621827
- Publisher
- Springer
- Year
- 2006
- Tongue
- English
- Weight
- 166 KB
- Volume
- 50
- Category
- Article
- ISSN
- 1434-6036
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This paper is concerned with traveling waves for the generalized Kadomtsev}Petviashvili equation (w y)31, t31, i.e. solutions of the form w(t, , y)"u( !ct, y). We study both, solutions periodic in x" !ct and solitary waves, which are decaying in x, and their interrelations. In particular, we prove
Recently, the (2 + 1)-dimensional modified Kadomtsev-Petviashvili (mKP) equation was decomposed into two known (1 + 1)-dimensional soliton equations by Dai and Geng [H.H. Dai, X.G. Geng, J. Math. Phys. 41 (2000) 7501]. In the present paper, a systematic and simple method is proposed for constructing