Analytic solutions of the (2 + 1)-dimensional nonlinear evolution equations using the sine–cosine method

• Published in: Applied mathematics and computation 2009-12, Vol.215 (8), p.3134-3139
• Main Authors: Taşcan, Filiz, Bekir, Ahmet
• Format: Article
• Language: English
• Subjects: (2 + 1)-Dimensional BKP equations; (2 + 1)-Dimensional Boussinesq equation; (2 + 1)-Dimensional breaking soliton equations; Exact sciences and technology; Exact solutions; Global analysis, analysis on manifolds; Mathematical analysis; Mathematics; Numerical analysis; Numerical analysis. Scientific computation; Partial differential equations; Partial differential equations, boundary value problems; Partial differential equations, initial value problems and time-dependant initial-boundary value problems; Sciences and techniques of general use; Sine–cosine method; Solitons; Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2009.09.027

In this paper, we establish exact solutions for (2 + 1)-dimensional nonlinear evolution equations. The sine–cosine method is used to construct exact periodic and soliton solutions of (2 + 1)-dimensional nonlinear evolution equations. Many new families of exact traveling wave solutions of the (2 + 1)-dimensional Boussinesq, breaking soliton and BKP equations are successfully obtained. These solutions may be important of significance for the explanation of some practical physical problems. It is shown that the sine–cosine method provides a powerful mathematical tool for solving a great many nonlinear partial differential equations in mathematical physics.