Generalized transformations and abundant new families of exact solutions for (2 + 1)-dimensional dispersive long wave equations
✍ Scribed by Zhenya Yan
- Publisher
- Elsevier Science
- Year
- 2003
- Tongue
- English
- Weight
- 539 KB
- Volume
- 46
- Category
- Article
- ISSN
- 0898-1221
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✦ Synopsis
It is well known that the general solutions of nonlinear evolution equations are very difficult to find. Searching for special explicit exact solutions, such as solitary wave solutions and periodic wave solutions, of nonlinear evolution equations in mathematical physics plays an important role in soliton theory [l-12]. Many powerful methods have been developed such as the Backlund transformation, the Darboux transformation, the Cole-Hopf transformation, the tanh method, the sine-cosine method, the Painleve method, the homogeneous balance method, and the similarity reduction method [l-l 11.
Recently, we extended the sine-cosine method [5] w ic h h was applied to a single equation to the case of a system of equations and applied it to find new solitary wave solutions for the variant Boussinesq [8] equations. The main idea of the sine-cosine method is as follows.