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RESEARCH PRODUCT

From first to fourth order rational solutions to the Boussinesq equation

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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 degree N (N + 1) − 2 in x and t, while the denominator is a polynomial of degree N (N + 1) in x and t. So we obtain a hierarchy of rational solutions depending on an integer N called the order of the solution. We construct explicit expressions of these rational solutions for N = 1 to 4.