Generation mechanism of rogue waves for the discrete nonlinear Schrödinger equation

2018 ◽  
Vol 83 ◽  
pp. 110-115 ◽  
Author(s):  
Min Li ◽  
Juan-Juan Shui ◽  
Tao Xu
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Rogue Waves ◽  
Nonlinear Schrodinger Equation ◽  
Generation Mechanism ◽  
Discrete Nonlinear Schrödinger Equation ◽  
Nonlinear Schrödinger

Rogue waves for an inhomogeneous discrete nonlinear Schrödinger equation in a lattice

2019 ◽  
Vol 33 (08) ◽  
pp. 1950090
Author(s):  
Xiao-Yu Wu ◽  
Bo Tian ◽  
Zhong Du ◽  
Xia-Xia Du
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Rogue Wave ◽  
Rogue Waves ◽  
Nonlinear Schrodinger Equation ◽  
External Potential ◽  
Discrete Nonlinear Schrödinger Equation ◽  
Nonlinear Schrödinger ◽  
Circular Pattern

Lattices are used in such fields as electricity, optics and magnetism. Under investigation in this paper is an inhomogeneous discrete nonlinear Schrödinger equation, which models the wave propagation in a lattice. Employing the Kadomtsev–Petviashvili (KP) hierarchy reduction, we obtain the rogue-wave solutions, and see that the rogue waves are affected by the coefficient of the on-site external potential. We see (1) the first-order rogue wave with one peak and two hollows; (2) the second-order rogue waves, each of which is with one peak or three humps; (3) the third-order rogue waves, each of which is with one peak or six humps, and those humps exhibit the triangular pattern, anti-triangular pattern and circular pattern. When the coefficient of the on-site external potential is a constant, the rogue waves periodically appear. When the coefficient of the on-site external potential monotonously changes, oscillations emerge on the constant background.

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