Ryogo Hirota

Nonlinear Partial Difference Equations III; Discrete Sine-Gordon Equation

A nonlinear partial difference equation which reduces to the sine-Gordon equation in the continuum limit, is obtained and solved by the method of dependent variable transformation. N -soliton solutions, the Backlund transformation and the inverse scattering form for this equation are presented.

Nonlinear Partial Difference Equations. I. A Difference Analogue of the Korteweg-de Vries Equation

A systematic method for isolating certain nonlinear partial difference equations that exhibit solitons is proposed. A nonlinear partial difference equation which approximates the Korteweg-de Vries equation in the weakly nonlinear and continuum limit, is obtained. N-soliton solutions, the Backlund transformation and the inverse scattering transform for this equation are presented.

Nonlinear Partial Difference Equations. V. Nonlinear Equations Reducible to Linear Equations

Difference analogues of the nonlinear partial differential equations that can be transformed into the linear equations are obtained, and exact solutions to the difference equations are presented. The nonlinear differential equations concerned are Liouvilles equation, Two-Wave interaction, the Riccati equation and the Burgers equation.

Exact N-Soliton Solution of Nonlinear Lumped Self-Dual Network Equations

Exact N -soliton solutions have been obtained for the nonlinear lumped self-dual network equations

Exact N-Soliton Solution of a Nonlinear Lumped Network Equation

Exact N -soliton solutions have been obtained for the nonlinear lumped network equation, (frac{partial^{2}}{partial t^{2}}log(1+V_{n}(t)){=}V_{n+1}(t)+V_{n-1}(t)-2V_{n}(t)). The solutions have the same functional forms as the N -soliton solution of the Korteweg-de Vries equation.

Difference Scheme of Soliton Equations

The study of discrete-time integrable systems is currently the focus of an intense activity1, 2, 3, 4.

A Simple Structure of Superposition Formula of the Bäcklund Transformation

Superposition formulae for soliton solutions are constructed from the Backlund transformation. The nonlinear evolution equations concerned are the Korteweg-de Vries (KdV), Boussinesq, two-dimensional KdV, modified KdV, Sine-Gordon and Toda equations. It is shown that the superposition formulae have a common simple structure when they are written in the bilinear forms.

N-Soliton Solutions of Nonlinear Network Equations Describing a Volterra System

N -soliton solutions of nonlinear network equations which originate from Volterras competition equations