ar X iv : s ol v - in t / 9 80 40 17 v 1 2 5 A pr 1 99 8 Travelling Wave Solutions in Nonlinear Diffusive and Dispersive Media

We investigate the presence of soliton solutions in some classes of nonlinear partial differential equations, namely generalized Korteweg-de Vries-Burgers, Korteveg-de VriesHuxley, and Korteveg-de Vries-Burgers-Huxley equations, which combine effects of diffusion, dispersion, and nonlinearity. We emphasize the chiral behavior of the travelling solutions, whose velocities are determined by the parameters that define the equation. For some appropriate choices, we show that these equations can be mapped onto equations of motion of relativistic 1 + 1 dimensional φ and φ field theories of real scalar fields. We also study systems of two coupled nonlinear equations of the types mentioned. PACS numbers: 03.40.-t, 52.35.Fp, 63.20.Ry This work is supported in part by funds provided by the U. S. Department of Energy (D.O.E.) under cooperative research agreement DE-FC02-94ER40818, and by Conselho Nacional de Desenvolvimento Cient́ıfico e Tecnológico, CNPq, Brazil. On leave from Departamento de F́ısica, Universidade Federal da Paráıba, Caixa Postal 5008, 58051970 João Pessoa, Paráıba, Brazil