Rational Solutions to the Boussinesq Equation
Résumé
Rational solutions to the Boussinesq equation are constructed as a quotient of two polynomials in xx and tt. For each positive integer NN, the numerator is a polynomial of degree N(N+1)−2N(N+1)−2 in xx and tt, while the denominator is a polynomial of degree N(N+1)N(N+1) in xx and tt. So we obtain a hierarchy of rational solutions depending on an integer NN called the order of the solution. We construct explicit expressions of these rational solutions for N=1N=1 to 44.