TÍTULO
EXISTENCE AND STABILITY OF SOLITARY WAVE SOLUTIONS OF THE BENJAMIN EQUATION
TIPO
Trabalho completo publicado em Journal of Differential Equations 152:136-159 (1999)
AUTOR
Jaime Angulo Pava
e-mail: angulo@ime.unicamp.br
DIRECCIÓN PARA CONTACTO
IMECC-UNICAMP-C.P. 6065
CEP 13083-970-Campinas
São Paulo, Brazil
RESUMEN
In this work we study certain properties of the
solutions of Benjamin's equation ([1], [2])
The approach in this paper is focused on the existence and stability of solitary-wave solutions of Eq. (1) using the concentration compactness method introduced by P.L. Lions ([4], [5]). The solitary-wave solutions of (1) are of the form , where is a dimensionless wave speed, and and its derivatives tend to zero as the variable approaches . Substituting this form of into (1) and integrating with respect to we obtain that satisfies the equation
References
[1] T.B. Benjamin, A new kind of solitary waves
J. Fluid Mechanics, 245:401-411, 1992
[2] T.B. Benjamin, Solitary and periodic waves of
a new kind Phil. Trans. R. Soc. lond. A, 354:1775-1806, 1996
[3] J.P. Albert, J.L. Bona and J.M. Restrepo, Solitary-wave
solutions of the Benjamin equation, Preprint 1996
[4] P.L. Lions, The concentration-compactness principle
in the calculus of variations. The locally compact case, part 1, Ann. Inst.
H. Poincaré, Anal. Non linéare, 1:109-145, 1984
[5] P.L. Lions, The concentration-compactness principle
in the calculus of variations. The locally compact case, part 2, Ann. Inst.
H. Poincaré, Anal. Non linéare, 4:223-283, 1984