Cipolatti, R.; Zumpichiatti, W. Orbitally stable standing waves for a system of coupled nonlinear Schrödinger equations. (English) Zbl 0964.35147 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 42, No. 3, 445-461 (2000). From the introduction: We consider the existence and the stability of standing waves (and specially the so-called ground state solutions) for the following system of one-dimensional nonlinear Schrödinger equations: \[ \begin{aligned} iu_t+ u_{xx}+ \alpha_1|u|^{p_1-2} u+\alpha_0|v|^{p_0} |u|^{p_0-2}u &= \delta v_{xx},\\ iv_t+ v_{xx}+ \alpha_2|v|^{p_2-2} v+\alpha_0|u|^{p_0- 2} v &=\delta u_{xx}, \end{aligned} \] where \(\alpha_j\geq 0\) \((j= 1,2)\), \(\alpha_0\in \mathbb{R}\), and \(|\delta|< 1\).Systems of this type appear in several branches of physics, such as in the study of interactions of waves with different polarizations or in the description of nonlinear modulations of two monochromate waves. Cited in 2 ReviewsCited in 17 Documents MSC: 35Q55 NLS equations (nonlinear Schrödinger equations) 78A60 Lasers, masers, optical bistability, nonlinear optics 37K45 Stability problems for infinite-dimensional Hamiltonian and Lagrangian systems Keywords:existence and stability of standing waves; ground state solutions; interactions of waves with different polarizations PDFBibTeX XMLCite \textit{R. Cipolatti} and \textit{W. Zumpichiatti}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 42, No. 3, 445--461 (2000; Zbl 0964.35147) Full Text: DOI