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Weakly non-local solitary wave solutions of a singularly perturbed Boussinesq equation
| Content Provider | Semantic Scholar |
|---|---|
| Author | Daripa, Prabir Dash, Ranjan K. |
| Copyright Year | 2001 |
| Abstract | We study the singularly perturbed (sixth-order) Boussinesq equation recently introduced by Daripa and Hua [Appl. Math. Comput. 101 (1999) 159]. This equation describes the bi-directional propagation of small amplitude and long capillary-gravity waves on the surface of shallow water for bond number less than but very close to 1/3. On the basis of far-field analyses and heuristic arguments, we show that the traveling wave solutions of this equation are weakly non-local solitary waves characterized by small amplitude fast oscillations in the far-field. Using various analytical and numerical methods originally devised to obtain this type of weakly non-local solitary wave solutions of the singularly perturbed (fifth-order) KdV equation, we obtain weakly non-local solitary wave solutions of the singularly perturbed (sixth-order) Boussinesq equation and provide estimates of the amplitude of oscillations which persist in the far-field. |
| Starting Page | 393 |
| Ending Page | 405 |
| Page Count | 13 |
| File Format | PDF HTM / HTML |
| DOI | 10.1016/S0378-4754(00)00288-3 |
| Alternate Webpage(s) | https://www.researchgate.net/profile/Ranjan_Dash/publication/2632148_Weakly_Non-local_Solitary_Wave_Solutions_of_a_Singularly_Perturbed_Boussinesq_Equation/links/0912f50bcc10592c61000000.pdf |
| Alternate Webpage(s) | http://www.math.tamu.edu/~Prabir.Daripa/pubs/preprints/spbe2.ps |
| Alternate Webpage(s) | http://www.math.tamu.edu/~daripa/pubs/reprints/mcs-01.pdf |
| Alternate Webpage(s) | https://doi.org/10.1016/S0378-4754%2800%2900288-3 |
| Volume Number | 55 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
