A Direct Method of Calculating Periodic Wave Solutions to Nonlinear Evolution Equations. I. Exact Two-Periodic Wave Solution

Abstract

It is shown that if a given nonlinear evolution equation is reduced to Hirota's single bilinear equation by the dependent variable transformation, it always has at least exact two-periodic wave (periodic analogue of two-soliton) solutions described by multi(two)-dimensional elliptic \( \vartheta \)-function.