A Cascade Algorithm for Solitary-Wave Solutions of the Benjamin Equation
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by Jianhong Shen
http://www.math.umn.edu/~jhshen/Mars/angeles.ps
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Abstract:
Following the recent work of Albert, Bona and Rostrep (SIAM J. Appl. Math., 59 (1999), pp. 2139-2161), we develop a nonlinear iterative scheme for the solitary-wave solutions to the Benjamin equation. It is implemented and analyzed both numerically and theoretically. The major advantages over the existing homotopy algorithm are its simplicity, eciency, generality, and the many properties it reveals about the exact solution, which has no simple closed form. An open problem is raised about the dynamic behavior of the related nonlinear iteration process. 1
Citations
| 16 | The stability of solitary waves – Benjamin - 1972 |
| 9 | Internal waves of permanent form in fluids of great depth – Benjamin - 1967 |
| 4 | Solitary-wave solutions of nonlinear problems – Benjamin, Bona - 1990 |
| 3 | Internal waves of permanent form in of great depth – Benjamin - 1967 |
| 3 | A new kind of solitary wave – Benjamin - 1992 |
| 3 | Existence and asymptotic properties of solitary-wave solutions of Benjamin-type equations – Bona - 1998 |
| 2 | Solitary-wave solutions of the Benjamin equation – Albert, Bona - 1999 |
| 2 | Solitary and periodic waves of a new kind – Benjamin - 1996 |
