Portal de Periódicos da CAPES

Painlevé integrability of two sets of nonlinear evolution equations with nonlinear dispersions

1999; Elsevier BV; Volume: 262; Issue: 4-5 Linguagem: Inglês

10.1016/s0375-9601(99)00580-0

1873-2429

Sen‐Yue Lou, WU Qi-xian,

Advanced Differential Equations and Dynamical Systems

It is proven that the nonlinear evolution equations (K(m,n) equations), ut+(um)x+(un)xxx=0 are Painlevé integrable for n=m−2 and n=m−1 with positive integer n. Especially, the solutions of the K(3,2) and K(4,2) models are single valued not only about a movable singularity manifold but also about a movable zero manifold. By using the general hodograph transformation, we know that there are five integrable K(m,n) models for negative n, K(−12,−12),K(32,−12),K(12,−12),K(−1,−2) and K(−2,−2), which are equivalent to the potential KdV, mKdV and CDF equations. However, the K(m,n) models for positive n are note equivalent to the known third order semilinear integrable ones.