Chapter 4 - The Infinite-Line Hirota Method

Abstract

This chapter discusses the infinite-line Hirota method. The Hirota direct method is developed to study soliton solutions and integrability in nonlinear wave equations. This approach provided an alternative theoretical tool for attacking soliton equations. The Hirota method is often applied to new equations whose integrability is uncertain, before applying the inverse scattering transform (IST) via Lax pairs and the inverse problem. Indeed, the Hirota method provides tools for actually deriving the Lax pair directly, providing a direct link to inverse scattering transform (IST). The direct method can be programmed for symbolic computation with REDUCE, Mathematica, and Maple so that much of the algebra can be accomplished with symbolic computation.