Hirota Bilinear Operator Research Articles

Lie Symmetry, Rational Solution and Bilinear Operator Structure for One and Two Dimensional Nonlinear Equations

We have systematized and extended the technique of Sym for obtaining the rational solutions of nonlinear equations in one and two space dimension through the use of Lie Symmetry and Hirota's bilinear operator, our method is easily extensible for higher dimensional integrable equations.

Lie symmetry, rational solution and bilinear operator structure for one- and two-dimensional nonlinear equations

The authors have systematised and extended the technique of Sym (1978) for obtaining the rational solutions of nonlinear equations in one and two space dimensions through the use of Lie symmetry and Hirota's bilinear operator. This method is easily extensible for higher-dimensional integrable equations.

A two-parameter Backlund transformation for the Boussinesq equation

A two-parameter Backlund transformation for the Boussinesq equation, utt-uxx-3(u2)xx-uxxxx=0, was obtained by using Hirota's bilinear operator. One can use the two arbitrary parameters in this Backlund transformation to derive the soliton solution, nonlinear superposition formula and infinitely many conservation laws.