Cauchy problem for the fifth order Kadomtsev-Petviashvili (KPII) equation

Pages: 887 - 905, Volume 5, Issue 4, December 2006

doi:10.3934/cpaa.2006.5.887       Abstract        Full Text (228.9K)       Related Articles

Pedro Isaza - Universidad Nacional de Colombia, Sede Medellín, A.A. 3840, Medellín, Colombia (email)
Juan López - Universidad de Pamplona, Pamplona, Colombia (email)
Jorge Mejía - Universidad Nacional de Colombia, Sede Medellín, A.A. 3840, Medellín, Colombia (email)

Abstract: It is proved that the initial value problem for the fifth order Kadomtsev-Petviashvili (KPII) equation is locally well-posed in the anisotropic Sobolev spaces $H^{s_1,s_2}( \mathbb R^2) $ with $s_1$>$-\frac{5}{4}$ and $s_2\geq 0,$ and globally well-posed in $H^{s,0}(\mathbb R^2) $ with $s$>$-\frac{4}{7}.$

Keywords:  Nonlinear dispersive equations, local solutions, global solutions.
Mathematics Subject Classification:  Primary: 35Q53; Secondary: 37K05.

Received: November 2005;      Revised: March 2006;      Published: September 2006.