Artículo
Mixed dispersion nonlinear Schrödinger equation in higher dimensions: Theoretical analysis and numerical computations
Autor/es | Stefanov, Atanas
Tsolias, Georgios A. Cuevas-Maraver, Jesús ![]() ![]() ![]() ![]() ![]() ![]() ![]() Kevrekidis, Panayotis G. |
Departamento | Universidad de Sevilla. Departamento de Física Aplicada I |
Fecha de publicación | 2022-06 |
Fecha de depósito | 2022-12-20 |
Publicado en |
|
Resumen | In the present work we provide a characterization of the ground states of a higher-dimensional quadratic-quartic model of the nonlinear Schrödinger class with a combination of a focusing biharmonic operator with either an ... In the present work we provide a characterization of the ground states of a higher-dimensional quadratic-quartic model of the nonlinear Schrödinger class with a combination of a focusing biharmonic operator with either an isotropic or an anisotropic defocusing Laplacian operator (at the linear level) and power-law nonlinearity. Examining principally the prototypical example of dimension d = 2, we find that instability arises beyond a certain threshold coefficient of the Laplacian between the cubic and quintic cases, while all solutions are stable for powers below the cubic. Above the quintic, and up to a critical nonlinearity exponent p, there exists a progressively narrowing range of stable frequencies. Finally, above the critical p all solutions are unstable. The picture is rather similar in the anisotropic case, with the difference that even before the cubic case, the numerical computations suggest an interval of unstable frequencies. Our analysis generalizes the relevant observations for arbitrary combinations of Laplacian prefactor b and nonlinearity power p. |
Agencias financiadoras | EU (FEDER program 2014–2020) and Consejería de Economía, Conocimiento, Empresas y Universidad de la Junta de Andalucía project P18-RT-3480 EU (FEDER program 2014–2020) and Consejería de Economía, Conocimiento, Empresas y Universidad de la Junta de Andalucía project US-1380977 MCIN/AEI/10.13039/501100011033 project PID2019-110430GB-C21 MCIN/AEI/10.13039/501100011033 project PID2020-112620GB-I00 |
Identificador del proyecto | P18-RT-3480
![]() US-1380977 ![]() PID2019-110430GB-C21 ![]() PID2020-112620GB-I00 ![]() |
Cita | Stefanov, A., Tsolias, G.A., Cuevas-Maraver, J. y Kevrekidis, P.G. (2022). Mixed dispersion nonlinear Schrödinger equation in higher dimensions: Theoretical analysis and numerical computations. Journal of Physics A: Mathematical and Theoretical, 55 (26), 265701. https://doi.org/10.1088/1751-8121/ac7019. |
Ficheros | Tamaño | Formato | Ver | Descripción |
---|---|---|---|---|
JPa_cuevas-maraver_2022_mixed.pdf | 545.8Kb | ![]() | Ver/ | |