666 research outputs found
Exotic dynamics of rogue waves in the scalar and coupled nonlocal nonlinear Schr\"{o}dinger equations
In this paper, general higher-order rogue wave solutions of the parity-time
() symmetric scalar and coupled nonlocal nonlinear
Schr\"{o}dinger equations (NLSEs) are calculated theoretically via a Darboux
transformation by a separation of variable technique. Furthermore, in order to
understand these solutions better, the main characteristics of the obtained
solutions are explored clearly and conveniently. Our results show that the
dynamics of these solutions exhibits rich patterns, most of which have no
counterparts in the corresponding local equations.Comment: 25 pages,18 figure
Lie symmetry analysis, conservation laws and analytical solutions for chiral nonlinear Schrödinger equation in (2 + 1)-dimensions
In this work, we consider the chiral nonlinear Schrödinger equation in (2 + 1)-dimensions, which describes the envelope of amplitude in many physical media. We employ the Lie symmetry analysis method to study the vector field and the optimal system of the equation. The similarity reductions are analyzed by considering the optimal system. Furthermore, we find the power series solution of the equation with convergence analysis. Based on a new conservation law, we construct the conservation laws of the equation by using the resulting symmetries. 
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