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Abstract
This paper mainly deals with the Cauchy problems for a deformed nonlinear Schrődinger equation, which is a new equation, denoted CH-NLS. Using a Galerkin-type approximation method, it is shown that this equation with is well-posed in Sobolev spaces
on both the line and the circle with continuous dependence on initial data. Moreover, the lower bound of the lifespan and the size of the solution are obtained.
Acknowledgements
The author thanks Professor Zhijun Qiao for his kind hospitality during her visit in the UTRGV.
Notes
No potential conflict of interest was reported by the author.
Additional information
Funding
This work was partially supported by the National Natural Science Foundation of China [grant number 11401223], NSF of Guangdong [grant number 2015A030313424]; the Science and Technology Program of Guangzhou [grant number 201607010005] and China Scholarship Council.