Abstract
The present paper investigates the higher-order Sawada-Kotera-type equation and the higher-order Lax-type equation in fluids. The Bell polynomials approach is employed to directly bilinearize the two equations. For the Lax-type equation, bilinear Bäcklund transformation, Lax pair, Darboux covariant Lax pair and infinitely many conservation laws are obtained by means of binary Bell polynomials. Moreover, based on its bilinear form, N-soliton solutions are also obtained. For the Sawada-Kotera-type equation, with the help of the Riemann theta function and Hirota bilinear method, its one periodic wave solution is obtained. A limiting procedure is presented to analyze in detail the relations between the one periodic wave solution and one soliton solution.
| Original language | English |
|---|---|
| Pages (from-to) | 533-551 |
| Number of pages | 19 |
| Journal | Nonlinear Analysis: Real World Applications |
| Volume | 31 |
| DOIs | |
| State | Published - 1 Oct 2016 |
Keywords
- Bell polynomials
- Hirota bilinear method
- Lax-type equation
- Sawada-Kotera-type equation
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