A nonlinear transformation of the dispersive long wave equations in (2+1) dimensions and its applications

A nonlinear transformation of the dispersive long wave equations in (2+1) dimensions is derived by using the homogeneous balance method. With the aid of the transformation given here, exact solutions of the equations are obtained

Supercritical Nonlinear Schr\"odinger equations: Quasi-Periodic Solutions

We construct time quasi-periodic solutions to the energy supercritical nonlinear Schr\"odinger equations on the torus in arbitrary dimensions. This introduces a new approach, which could have general applicability.Comment: 62 pages; Duke Math. J. (to appear

About "On certain incomplete statistics" by Lima et al

Lima et al recently claim that ({\em Chaos, Solitons & Fractals,} 2004;19:1005)the entropy for the incomplete statistics based on the normalization$\sum_ip_i^q=1$ should be $S=-\sum_ip_i^{2q-1}\ln_qp_i$ instead of$S=-\sum_ip_i^{q}\ln_qp_i$ initially proposed by Wang. We indicate here that thisconclusion is a result of erroneous use of temperature definition for the incompletestatistics