Rational Solutions to the Boussinesq Equation

Authors : Pierre GAİLLARD

Pages : 1-4

Doi:10.33401/fujma.512333

View : 18 | Download : 10

Publication Date : 2019-06-17

Article Type : Research Paper

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 degree $Ninsert ignore into journalissuearticles values(N+1);-2$ in $x$ and $t$, while the denominator is a polynomial of degree $Ninsert ignore into journalissuearticles values(N+1);$ 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 $4$.
Keywords : Boussinesq equation, Rational solutions, Rogue wave