Solutions of the Boussinesq equation
The rational solutions of the Boussinesq equation (mainly those which decay to zero when x goes to infinity) are studied. The solution is written in terms of a function which is assumed to have a polynomial form, and the coefficients are computed. It is interesting to emphasize that rational solutions exist only for some value of maximal degree of the polynomials. Finally, the solutions are computed using the Bäcklund transformations.
scientific article; zbMATH DE number 3992052
scientific article