Boussinesq Equation

The linear Boussinesq equation is the partial differential equation

(1)

(Whitham 1974, p. 9; Zwillinger 1997, p. 129). The nonlinear Boussinesq equation is

(2)

(Calogero and Degasperis 1982; Zwillinger 1997, p. 130). The modified Boussinesq equation is

(3)

(Clarkson 1986; Zwillinger 1997, p. 132).

REFERENCES:

Calogero, F. and Degasperis, A. Spectral Transform and Solitons: Tools to Solve and Investigate Nonlinear Evolution Equations.New York: North-Holland, 1982.

Clarkson, P. A. "The Painlevé Property, a Modified Boussinesq Equation and a Modified Kadomtsev-Petviashvili Equation." Physica D 19, 447-450, 1986.

Whitham, G. B. Linear and Nonlinear Waves. New York: Wiley, 1974.

Zwillinger, D. Handbook of Differential Equations, 3rd ed. Boston, MA: Academic Press, pp. 129-130, 1997.