Abstract
We investigate the asymptotic behaviour of the localized solitarywaves for the generalized Kadomtsev-Petviashvili equations. Inparticular, we compute their first order asymptotics in anydimension $N \geq 2$.
Highlights
1.1 Motivation and main resultsThe present paper deals with the solitary waves for the generalised Kadomtsev-Petviashvili equations∂tu + up∂1u + ∂13u − N ∂j uj = 0, ∀j ∈ j=2{2, . . . , N }, ∂1uj = ∂ju. (1)
Theorem 1 is optimal for any non-trivial solitary wave when m is an odd number
There is only one possible asymptotics for all the solitary waves with the same energy. This seems to be a further evidence of the uniqueness of non-trivial solitary waves in the case of the standard Kadomtsev-Petviashvili equation: we believe that this new evidence could be a useful step towards the resolution of this problem, which is still open to our knowledge
Summary
Theorem 1 is optimal for any non-trivial solitary wave when m is an odd number (which holds for the standard Kadomtsev-Petviashvili equation). There may be non-trivial solitary waves whose decay rate is higher than r−N This may happen if the function v∞ is identically equal to 0, that is if v(x)p+1dx = 0. There is only one possible asymptotics for all the solitary waves with the same energy This seems to be a further evidence of the uniqueness of non-trivial solitary waves (up to translations) in the case of the standard Kadomtsev-Petviashvili equation: we believe that this new evidence could be a useful step towards the resolution of this problem, which is still open to our knowledge
Sign-in/Register to view highlights & summary 
Published Version
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
