Rational Solutions to the Boussinesq Equation

Abstract

Rational solutions to the Boussinesq equation are constructed as a quotient of two polynomials in x and t. For each positive integer N, the numerator is a polynomial of degreeN(N +1)−2 in x and t, while the denominator is a polynomial of degree N(N +1) in x andt. So we obtain a hierarchy of rational solutions depending on an integer N called the orderof the solution. We construct explicit expressions of these rational solutions for N = 1 to 4.