scholarly journals Numerical simulation of resonant tunneling of fast solitons for the nonlinear Schrödinger equation

2011 ◽  
Vol 29 (4) ◽  
pp. 1637-1649 ◽  
Author(s):  
Walid K. Abou Salem ◽  
◽  
Xiao Liu ◽  
Catherine Sulem ◽  
Keyword(s):  
Numerical Simulation ◽  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Resonant Tunneling ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger

scholarly journals Dynamics of Different Nonlinearities to the Perturbed Nonlinear Schrödinger Equation via Solitary Wave Solutions with Numerical Simulation

2021 ◽  
Vol 5 (4) ◽  
pp. 213
Author(s):  
Asim Zafar ◽  
Muhammad Raheel ◽  
Muhammad Qasim Zafar ◽  
Kottakkaran Sooppy Nisar ◽  
Mohamed S. Osman ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Solitary Wave ◽  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Power Law ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Solitary Wave Solutions ◽  
Nonlinear Schrödinger ◽  
Wave Solutions

This paper investigates the solitary wave solutions for the perturbed nonlinear Schrödinger equation with six different nonlinearities with the essence of the generalized classical derivative, which is known as the beta derivative. The aforementioned nonlinearities are known as the Kerr law, power, dual power law, triple power law, quadratic–cubic law and anti-cubic law. The dark, bright, singular and combinations of these solutions are retrieved using an efficient, simple integration scheme. These solutions suggest that this method is more simple, straightforward and reliable compared to existing methods in the literature. The novelty of this paper is that the perturbed nonlinear Schrödinger equation is investigated in different nonlinear media using a novel derivative operator. Furthermore, the numerical simulation for certain solutions is also presented.

Resonant Tunneling of Fast Solitons through Large Potential Barriers

2011 ◽  
Vol 63 (6) ◽  
pp. 1201-1219 ◽  
Author(s):  
Walid K. Abou Salem ◽  
Catherine Sulem
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Resonant Tunneling ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
One Dimension ◽  
Potential Barriers ◽  
Nonlinear Schrödinger ◽  
Large Potential

AbstractWe rigorously study the resonant tunneling of fast solitons through large potential barriers for the nonlinear Schrödinger equation in one dimension. Our approach covers the case of general nonlinearities, both local and Hartree (nonlocal).

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