Periodic and solitary traveling wave solutions for the generalized Kadomtsev–Petviashvili equation

✍ Scribed by A. A. Pankov; K. Pflüger

• Publisher: John Wiley and Sons
• Year: 1999
• Tongue: English
• Weight: 164 KB
• Volume: 22
• Category: Article
• ISSN: 0170-4214
• DOI: 10.1002/(sici)1099-1476(199906)22:9<733::aid-mma14>3.0.co;2-s

✦ Synopsis

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 the existence of a sequence of k-periodic solutions, k3-, which is uniformly bounded in norm and converges to a solitary wave in a suitable topology. This result also holds for the corresponding ground states, i.e. solutions with minimal energy.