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Related Experiment Video

Updated: May 9, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Rogue wave solutions to the generalized nonlinear Schrödinger equation with variable coefficients.

Wei-Ping Zhong¹, Milivoj R Belić, Tingwen Huang

¹Department of Electronic and Information Engineering, Shunde Polytechnic, Guangdong Province, Shunde 528300, China. zhongwp6@126.com

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|July 16, 2013

Summary

Researchers transformed a generalized nonlinear Schrödinger (NLS) equation to a standard form, constructing rogue wave solutions like Ma breathers for the original equation. These findings may enable new experiments and applications.

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Area of Science:

Nonlinear dynamics
Mathematical physics
Wave phenomena

Background:

The generalized nonlinear Schrödinger (NLS) equation with variable coefficients describes complex wave phenomena.
Finding exact solutions for such equations is challenging but crucial for understanding wave behavior.

Purpose of the Study:

To construct rogue wave solutions for the generalized nonlinear Schrödinger (NLS) equation.
To investigate the properties and controllability of these solutions.

Main Methods:

A similarity transformation was employed to simplify the generalized NLS equation to the standard NLS equation.
Known rogue wave solutions of the standard NLS equation were transformed back to the original equation.

Main Results:

Ma breathers, along with first- and second-order rogue wave solutions, were successfully constructed for the generalized NLS equation.
Specific solution properties were analyzed, and their controllability was discussed.

Conclusions:

The study provides a method for generating complex rogue wave solutions for variable-coefficient NLS equations.
The findings may facilitate experimental studies and potential applications of nonlinear waves.