In this paper, we consider the existence of a type of stationary wave of a system of two coupled Schrödinger equations with variable coefficients, which can be employed to describe the interaction among propagating modes in nonlinear optics and Bose-Einstein condensates (BECs), for instance. To prove existence of these solutions, we use some existing fixed point theorems for completely continuous operators defined in a cone in a Banach space. Furthermore, some numerical approximations of stationary waves are computed by using a spectral collocation technique combined with a Newton’s iteration.
CITATION STYLE
Muñoz Grajales, J. C., & Vargas, L. F. (2019). Existence and Numerical Computation of Standing Wave Solutions for a System of Two Coupled Schrödinger Equations. In Springer Proceedings in Mathematics and Statistics (Vol. 275, pp. 191–206). Springer New York LLC. https://doi.org/10.1007/978-3-030-05657-5_12
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