Abstract
In this work, the Wronskian determinant technique is performed to(2+1)-dimensional non-local Ito equation in the bilinear form. First, we obtainsome su¢ cient conditions in order to show Wronskian determinant solves the(2+1)-dimensional non-local Ito equation. Second, rational solutions, solitonsolutions, positon solutions, negaton solutions and their interaction solutionswere deduced by using the Wronskian formulations
Highlights
The nonlinear evolution equations (NLEEs) model abundant physical processes which occur in the nature
Rational solutions, soliton solutions, positon solutions, negaton solutions and their interaction solutions were deduced by using the Wronskian formulations
In the literature a plenty of analytic and numerical methods were developed such as inverse scattering transform, Hirota bilinear method, the Riccati equation expansion method, the sine–cosine method, the tanh sech method, G0=G expansion method, Adomian decomposition method, He’s variational principle, Lie symmetry method and many more ([1],[3]-[6]-[7], [8],[14], [19]-[20], [22]-[23])
Summary
The nonlinear evolution equations (NLEEs) model abundant physical processes which occur in the nature. Investigating and obtaining solutions of these type equations have an extremely important place in nonlinear science. It is demonstrated in [12] that for each type of Jordan blocks of the coe¢ cient matrix J ( ij), there exist special sets of eigenfunctions These functions were used to generate rational solutions, solitons, positons, negatons, breathers, complexitons and their interaction solutions. The obtained solution formulas of the representative systems allow us to construct more general Wronskian solutions than rational solutions, positons, negatons, complexitons and their interaction solutions. Interaction solutions among negatons, positons, rational solutions and complexitons are a class of much more general and complicated solutions to soliton equations, in the category of elementary function solutions.
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