Asymptotics for Large Time of Global Solutions to the Generalized Kadomtsev–Petviashvili Equation
✍ Scribed by Nakao Hayashi; Pavel I. Naumkin; Jean-Claude Saut
- Publisher
- Springer
- Year
- 1999
- Tongue
- English
- Weight
- 126 KB
- Volume
- 201
- Category
- Article
- ISSN
- 0010-3616
No coin nor oath required. For personal study only.
📜 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
We study the asymptotic behavior for large time of solutions to the Cauchy problem for the generalized Korteweg de Vries (gKdV) equation u t + ( |u| \&1 u) x + 1 3 u xxx =0, where x, t # R when the initial data are small enough. If the power \ of the nonlinearity is greater than 3 then the solution
An exact 1-soliton solution of the generalized Camassa-Holm Kadomtsev-Petviashvili equation is obtained in this paper by the solitary wave ansatze. This solution is a generalized form of the solution that is obtained in earlier works.
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 ex