Solitary wave solutions of nonlinear evolution and wave equations using a direct method and MACSYMA

@article{Hereman1990SolitaryWS,
  title={Solitary wave solutions of nonlinear evolution and wave equations using a direct method and MACSYMA},
  author={Willy A. Hereman and Masanori Takaoka},
  journal={Journal of Physics A},
  year={1990},
  volume={23},
  pages={4805-4822}
}
The direct algebraic method for constructing travelling wave solutions on nonlinear evolution and wave equations has been generalized and systematized. The class of solitary wave solutions is extended to analytic (rather than rational) functions of the real exponential solutions of the linearized equation. Expanding the solutions in an infinite series in these real exponentials, an exact solution of the nonlinear PDE is obtained, whenever the series can be summed. Methods for solving the… 
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