scholarly journals The Gerdjikov‐Ivanov–type derivative nonlinear Schrödinger equation: Long‐time dynamics of nonzero boundary conditions

2019 ◽  
Vol 42 (14) ◽  
pp. 4839-4861
Author(s):  
Boling Guo ◽  
Nan Liu
Keyword(s):  
Schrödinger Equation ◽  
Boundary Conditions ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Time Dynamics ◽  
Long Time ◽  
Derivative Nonlinear Schrödinger Equation ◽  
Nonzero Boundary ◽  
Long Time Dynamics

scholarly journals Multiple Soliton Interactions on the Surface of Deep Water

Fluids ◽  
2020 ◽  
Vol 5 (2) ◽  
pp. 65 ◽  
Author(s):  
Dmitry Kachulin ◽  
Alexander Dyachenko ◽  
Sergey Dremov
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Deep Water ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Time Dynamics ◽  
Nonlinear Schrödinger ◽  
Long Time ◽  
Long Time Dynamics ◽  
Number Of Particles

The paper presents the long-time dynamics with multiple collisions of breathers in the super compact Zakharov equation for unidirectional deep water waves. Solutions in the form of breathers were found numerically by the Petviashvili method. In the terms of envelope and the assumption of the narrow spectral width the super compact equation turns into the well known exact integrable model—nonlinear Schrödinger equation, and the breather solution in this case turns into envelope soliton. The results of numerical simulations show that two main scenarios of long-time dynamics occur during numerous collisions of breathers. In the first case, one of the breathers regularly takes a number of particles from the other one at each collision and in the second one a structure resembling the bi-soliton solution of nonlinear Schrödinger equation arises during the collision. Despite these scenarios, it is shown that after numerous collisions the only one breather having initially a larger number of particles remains.

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