A New Class of Soliton Solutions for the (Modified) Kadomtsev-Petviashvili Equation
β Scribed by Walter Renger
- Publisher
- John Wiley and Sons
- Year
- 1999
- Tongue
- English
- Weight
- 675 KB
- Volume
- 202
- Category
- Article
- ISSN
- 0025-584X
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β¦ Synopsis
We construct solutions of the Kadomtsev-Petviashvili equation and its counterpart, the modified Kadomtsev-Petviashvili equation, with an infinite number of solitons by a careful armination of the limits of N -soliton solutions as N --t OQ. We give sufficient conditions to ensure that these limits exist and satisfy the (modified) Kadomtsev-Petviashvili equation.
π SIMILAR VOLUMES
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
Let K be an algebraic number field such that all the embeddings of K into C are real. We denote by O K the ring of algebraic integers of K. Let F(X, Y) be an irreducible polynomial in K[X, Y ]&K[Y ] of total degree N and of degree n>0 in Y. We denote by F N (X, Y ) its leading homogeneous part. Supp