Travelling Wave Solutions in Nonlinear Diffusive and Dispersive Media

Details Travelling Wave Solutions in Nonlinear Diffusive and Dispersive Media Travelling Wave Solutions in Nonlinear Diffusive and Dispersive Media

1998-04-25

arxiv.org/abs/solv-int/9804017v1

Physics

Condensed Matter

10 pages, Latex

Scientific paper

We investigate the presence of soliton solutions in some classes of nonlinear partial differential equations, namely generalized Korteweg-de Vries-Burgers, Korteveg-de Vries-Huxley, 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 phi^{4} and phi^{6} field theories of real scalar fields. We also study systems of two coupled nonlinear equations of the types mentioned.

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