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In this work, we study the quantum Zakharov system which describes the nonlinear interaction between high-frequency quantum Langmuir waves and low-frequency quantum ion-acoustic waves. We show the existence and the stability of the standing waves of quantum Zakharov system for the spacial dimensions d = 1 , 2 , 3 . [ABSTRACT FROM AUTHOR]

This paper is a continuation of our previous study [13] on the long time behavior of solution to the nonlinear Schrödinger equation with higher order anisotropic dispersion (4NLS). We prove the long range scattering for (4NLS) with the quadratic nonlinearity in two dimensions. More precisely, for a given asymptotic profile u + , we construct a solution to (4NLS) which converges to u + as t → ∞ , where u + is given by the leading term of the solution to the linearized equation of (4NLS) with a logarithmic phase correction. [ABSTRACT FROM AUTHOR]