International Journal of Mathematics and Mathematical Sciences
Volume 6 (1983), Issue 2, Pages 395-402

Generalized function treatment of the Alfvén-gravity wave problem

L. Debnath and K. Vajravelu

Department of Mathematics, East Carolina University, Greenville 27834, N.C., USA

Received 30 September 1982; Revised 12 April 1983

Copyright © 1983 L. Debnath and K. Vajravelu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A study is made of the steady-state Alfvén-gravity waves in an inviscid incompressible electrically conducting fluid with an interface due to a harmonically oscillating pressure distribution acting on the interface. The generalized function method is employed to solve the problem in the fluid of infinite, finite and shallow depth. A unique solution of physical interest is derived by imposing the Sommerfeld radiation condition at infinity. Several limiting cases of physical interest are obtained from the present analysis. The physical significance of the solutions and their limiting cases are discussed.