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Integrable nonautonomous nonlinear Schrödinger equations are equivalent to the standard autonomous equation
1Theory Group, Saha Institute of Nuclear Physics, & CAMCS, Calcutta, India. anjan.kundu@saha.ac.in
Summary
Novel nonautonomous nonlinear Schrödinger equations are not new. These systems are equivalent to the standard autonomous equation, which explains their integrability and rich properties.
Area of Science:
- Mathematical Physics
- Nonlinear Dynamics
Background:
- The literature features nonautonomous nonlinear Schrödinger equations presented as novel integrable systems.
- These systems are claimed to possess rich mathematical properties and applications.
Purpose of the Study:
- To critically evaluate the novelty and integrability of recently published nonautonomous nonlinear Schrödinger equations.
- To demonstrate the relationship between these purported novel systems and the established autonomous nonlinear Schrödinger equation.
Main Methods:
- Mathematical analysis of the structure of nonautonomous nonlinear Schrödinger equations.
- Demonstration of equivalence transformations between nonautonomous and autonomous forms.
- Analysis of integrability features through established mathematical techniques.
Main Results:
- All investigated nonautonomous nonlinear Schrödinger equations are mathematically equivalent to the standard autonomous nonlinear Schrödinger equation.
- The claimed novelty of these systems is disproven.
- The integrability properties are shown to be inherited directly from the standard autonomous equation.
Conclusions:
- The purported novel nonautonomous nonlinear Schrödinger equations are not new discoveries.
- Their integrability and rich properties are trivial consequences of their equivalence to the standard autonomous equation.
- This finding clarifies the landscape of integrable nonlinear Schrödinger systems.
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