Abstract
In this paper, bi-solitons, breather solution family and rogue waves for the (2+1)-Dimensional nonlinear Schrodinger equations are obtained by using Exp-function method. These solutions derived from one unified formula which is solution of the standard (1+1) dimension nonlinear Schrodinger equation. Further, based on the solution obtained by other authors, higher-order rational rogue wave solution are obtained by using the similarity transformation. These results greatly enriched the diversity of wave structures for the (2+1)-dimensional nonlinear Schrodinger equations.
Highlights
IntroductionWe continue to investigate the existence of rogue waves and their structures for the (2+1)-dimensional nonlinear Schrodinger equations
The (2+1)-dimensional nonlinear Schrodinger equations are expressed as iut = uxy + γ2uv, vx = 2(|u|2)y, (1.1)
Rogue wave phenomenon become a hot topic for many researchers
Summary
We continue to investigate the existence of rogue waves and their structures for the (2+1)-dimensional nonlinear Schrodinger equations. I. When 4c22 − b24 > 0 and γ2 = 1, solutions(2.9) become the following forms which are called Akhmediev breather solitons u(x, y, t). When b4 = ib and γ2 = 1, solutions(2.9) become the following forms which are called Ma breather solitons u(x, y, t). 1, higher-order rational rogue wave solutions of equation(2.2) are given by Akhmediev [2, 3]. [2, 3], we obtained higher-order rational rogue wave solutions of equation(2.2) as follows: u(z, t) =. 0 and z k1x+k2y into (3.6), we have higher-order rational rogue wave solutions of equations(1.1) which are written as.
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