2005 Nonlinear Waves

effects of variable environment and damping In many physical situations it is necessary to take account of the fact that nonlinear waves propagate through a variable environment. Examples include shallow-water waves moving over an uneven bottom, internal gravity waves in lakes of varying cross-section, long waves in rotating fluids contained in cylindrical tubes, and many others. Typically, the problems of this type imply that the coefficients in the governing nonlinear dispersive wave equation are varying in time and/or space. Here we consider some problems modeled by the variable-coefficient KdV equation ut + α(t)uux + β(t)uxxx = 0, (1) I In the modelling of the variable environment effects, the variables x, t in equation (1) are not necessarily the same physical space and time coordinates as in the traditional interpretation of the KdV equation