Higher Order Solution of Nonlinear Waves. I. Cnoidal Wave in Unstable and Dissipative Media

抄録

An equilibrium solution is obtained analytically for a nonlinear and dispersive wave with weakly unstable and dissipative conditions. Based on a cnoidal wave solution to the Korteweg-de Vries (K-dV, for short) equation, the second order solution is obtained by taking into account the unstable and dissipative effects. These effects impose some restrictions on the cnoidal wave even when the effects are weak, that is, the relation between the wave-length and amplitude of the cnoidal wave appears which is not the case for the K-dV equation. The explicit second order solution brings about asymmetry in the wave form.