Multiple-soliton solutions for the generalized (1+1)-dimensional and the generalized (2+1)-dimensional Ito equations

The generalized (1+1)-dimensional and the generalized (2+1)-dimensional Ito equations, obtained by introducing a new type of bilinearism, are studied. The tanh-coth method is used to obtain single soliton solutions and periodic solutions for the Ito equations. The Hirota bilinear method is used to determine the multiple-soliton solutions of sech-squared type for these equations. New entirely solutions are obtained. The analysis emphasizes the power of the two methods and its capability of handling completely integrable equations. (C) 2008 Elsevier Inc. All rights reserved.