We present new analytical solutions to the hyperbolic generalization of Burgers equation, describing interaction of the wave fronts. To obtain them, we employ a modified version of the Hirota method.

The dispersionless differential Fay identity is shown to be equivalent to a kernel expansion providing a universal algebraic characterization and solution of the dispersionless Hirota equations. Some calculations based on D-bar data of the action are also indicated.

We show that we can also apply the Hirota method to some nonintegrable equations. For this purpose, we consider the extensions of the Kadomtsev-Petviashvili (KP) and the Boussinesq (Bo) equations. We present several solutions of these equations.

The solitons and kinks of the generalized sl(3,C) sine-Gordon (GSG) model are explicitly obtained through the hybrid of the Hirota and dressing methods in which the tau functions play an important role. The various properties are investigated, such as the potential vacuum structure, the soliton and kink solutions and the soliton masses formulae. As a reduced submodel we obtain the double sine-G...

It is renowned that Hirota–Satsuma–Ito (HSI) equation widely used to study wave dynamics of shallow water. In this work, two new HSI-like equations are investigated which could be extended diversify problems in natural phenomena and give admirable contributions by applying the generalized exponential rational function method (GERFM). With aid symbolic calculations, various constraints on free p...