engleski

Localized local maxima for non-negative ground state solution of nonlinear Schrodinger equation with non- monotone external potential

Non-negative ground state solution $u(x)$ of the nonlinear Schr\"{; ; o}; ; dinger equation with non-monotone potential is studied. The existence of local maxima of $u(x)$ which are attained on given intervals in one-dimensional space variable $x$ is shown. Next, it is proved that the stationary point of $u(x)$ per one interval is unique. The co-existence of the local extrema of ground state solution and external potential on the same interval is considered too. It has been already visualized in some numerical simulations of approximate or exact solutions published by other authors. The nonlinear term allows to be of the general attractive or a special repulsive type. In the attractive case, the main result represents the mathematical verification for localized local maxima in one-dimensional space variable of the particle density of solitary wave in Bose-Einstein condensates with attractive atom-atom interaction.

Schrodinger equation ; ground state solution ; extrema ; non-monotonic behaviour ; particle density ; Bose-Einstein condensates

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