Dynamical systems theory for nonlinear evolution equations.

We observe that the fully nonlinear evolution equations of Rosenau and Hymann, often abbreviated as K(n,m) equations, can be reduced to Hamiltonian form only on a zero-energy hypersurface belonging to some potential function associated with the equations. We treat the resulting Hamiltonian equations by the dynamical systems theory and present a phase-space analysis of their stable points. The results of our study demonstrate that the equations can, in general, support both compacton and soliton solutions. For the K(2,2) and K(3,3) cases one type of solutions can be obtained from the other by continuously varying a parameter of the equations. This is not true for the K(3,2) equation for which the parameter can take only negative values. The K(2,3) equation does not have any stable point and, in the language of mechanics, represents a particle moving with constant acceleration.

Comparative evaluation of hepatitis C virus infection in serum and liver tissue of patients with chronic liver disease by reverse transcription-polymerase chain reaction.

OBJECTIVE: To undertake a comparative evaluation of diagnostic modalities used in the detection of hepatitis C virus (HCV) infection by serum antibody in ELISA and HCV-RNA in the serum as well as in the liver tissue of the same patients with chronic liver disease by reverse transcription-polymerase chain reaction (RT-PCR). METHODS: Thirty-five subjects comprising 30 cases of cirrhosis of the liver and five cases of chronic hepatitis were included in the study group. The criteria for including the subjects in the study were the availability and quality of serum and liver samples. Serologic ELISA tests for HCV antibody as well as HBsAg and anti-HBc IgG for hepatitis B virus (HBV) were performed on the patient's sera, while RT-PCR was carried out with RNA extracted from both serum and liver biopsies of the patients. Primer sequences selected from the conserved NS5 region of the HCV genome were used in RT-PCR. RESULTS: Of 30 cases of cirrhosis studied, five (16.6%) were anti-HCV antibody positive, while seven (23.3%) were positive for HCV RNA in serum and 10 (33.3%) were positive in liver tissue. One of the anti-HCV antibody-positive patients was negative for HCV RNA in both liver and serum by PCR. All seven patients who showed positivity for HCV RNA in serum were also positive for HCV RNA in the liver. Another three cirrhosis cases (10%) found to be HCV positive in liver tissue were negative for both antibody and HCV RNA in serum. Of the five cases of chronic hepatitis, two (40%) were found to be positive by all three tests. HCV was found to be more prevalent in HBV-infected cases (8/18; 44.5%). However, two of the three cirrhotic patients who showed HCV positivity only in liver PCR tested negative for HBV surface antigen. CONCLUSIONS: RT-PCR detection of HCV RNA in liver tissue is of significant clinical importance and is more reliable than RT-PCR in serum or antibody tests by ELISA. RT-PCR can effectively complement antibody tests for reliable diagnosis, since assessment of HCV positivity by a single test seems to be inadequate. The frequent association of HCV infection with HBV suggests that hepatitis B and C viruses may share similar modes of transmission in India.