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The higher order nonlinear Schr\"{o}dinger equation with quadratic nonlinearity on the real axis

Analysis of PDEs 2022-03-29 v1

Abstract

The initial value problem is considered for a higher order nonlinear Schr\"odinger equation with quadratic nonlinearity. Results on existence and uniqueness of weak solutions are obtained. In the case of an effective at infinity additional damping large-time decay of solutions without any smallness assumptions is also established. The main difficulty of the study is the non-smooth character of the nonlinearity.

Keywords

Cite

@article{arxiv.2203.14830,
  title  = {The higher order nonlinear Schr\"{o}dinger equation with quadratic nonlinearity on the real axis},
  author = {Andrei V. Faminskii},
  journal= {arXiv preprint arXiv:2203.14830},
  year   = {2022}
}

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41 pages