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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
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.
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.
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