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Nonlinear Schrödinger equations with the third order dispersion on modulation spaces

Mahendra Panthee (UNICAMP)

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We consider the initial value problems (IVPs) associated to the extended nonlinear Schr"odinger (e-NLS) equation and the higher order nonlinear Schr"odinger (h-NLS) equation for given data in the modulation space $M_s^{2,p}(R)$. We derive a trilinear estimate for functions with negative Sobolev regularity and use it in the contraction mapping principle to prove that the IVPs associated to the e-NLS equation and the h-NLS equation are locally well-posed for $s>-\frac14$ and $s\geq\frac14$ respectively.

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