The Periodic Wave Solution For Nonisospectral KP Equation And Variable Coefficient KdV Equation

In this paper, we consider the periodic wave solutions for nonisospectral KP equation and variable coefficient KdV equation by Hirota method and Riemann theta function. First, through a dependent variable transformation, nonisospectral KP equation and vari-able coefficient KdV equation can be written into their bilinear equations. By the bilinear equations, not only we can get their soliton solutions, but also we can obtain their pe-riodic wave solutions through Hirota method and Riemann theta function. Second, a limiting procedure is presented to analyze asymptotic properties of the periodic solutions. Relations between the periodic solutions and the well-known soliton solutions are estab-lished. It is shown that the periodic solutions tend to the soliton solutions under a small amplitude limit.