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Finite difference discretization with variable mesh of the Schrodinger equation in a variable domain

Georgios D. Akrivis, Vassilios A. Dougalis (1990)

Δελτίο της Ελληνικής Μαθηματικής Εταιρίας

Finite-energy sign-changing solutions with dihedral symmetry for the stationary nonlinear Schrödinger equation

Monica Musso, Frank Pacard, Juncheng Wei (2012)

Journal of the European Mathematical Society

We address the problem of the existence of finite energy solitary waves for nonlinear Klein-Gordon or Schrödinger type equations $Δ u - u + f (u) = 0$ in $ℝ^{N}$ , $u \in H^{1} (ℝ^{N})$ , where $N \geq 2$ . Under natural conditions on the nonlinearity $f$ , we prove the existence of $𝑖𝑛𝑓𝑖𝑛𝑖𝑡𝑒𝑙𝑦𝑚𝑎𝑛𝑦𝑛𝑜𝑛𝑟𝑎𝑑𝑖𝑎𝑙𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛𝑠$ in any dimension $N \geq 2$ . Our result complements earlier works of Bartsch and Willem $(N = 4 𝚘𝚛 N \geq 6)$ and Lorca-Ubilla $(N = 5)$ where solutions invariant under the action of $O (2) \times O (N - 2)$ are constructed. In contrast, the solutions we construct are invariant under the action of $D_{k} \times O (N - 2)$ where $D_{k} \subset O (2)$ denotes the dihedral group...

Fourier Transform Restriction Phenomena for Certain Lattice Subsets and Applications to Nonlinear Evolution Equations, Part II: The KDV Equation.

J. Bourgain (1993)

Geometric and functional analysis

Fourier Transform Restriction Phenomena for Certain Lattice Subsets and Applications to Nonlinear Evolution Equations, Part I: Schrödinger Equations.

J. Bourgain (1993)

Geometric and functional analysis

Fourth order time-stepping for low dispersion Korteweg-de Vries and nonlinear Schrödinger equations.

Klein, Christian (2007)

ETNA. Electronic Transactions on Numerical Analysis [electronic only]

Fractal analysis of Hopf bifurcation for a class of completely integrable nonlinear Schrödinger Cauchy problems.

Milišic, Josipa Pina, Žubrinić, Darko, Županović, Vesna (2010)

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

Displaying 1 – 9 of 9

Finite difference discretization with variable mesh of the Schrodinger equation in a variable domain

Finite-energy sign-changing solutions with dihedral symmetry for the stationary nonlinear Schrödinger equation

Foliation of phase space for the cubic non-linear Schrödinger equation

Fonctionnelles de Ginzburg-Landau et espaces de configurations de particules positives et négatives

Formulation variationnelle de systèmes Schrödinger-Poisson en dimension $d \leq 3$

Fourier Transform Restriction Phenomena for Certain Lattice Subsets and Applications to Nonlinear Evolution Equations, Part II: The KDV Equation.

Fourier Transform Restriction Phenomena for Certain Lattice Subsets and Applications to Nonlinear Evolution Equations, Part I: Schrödinger Equations.

Fourth order time-stepping for low dispersion Korteweg-de Vries and nonlinear Schrödinger equations.

Fractal analysis of Hopf bifurcation for a class of completely integrable nonlinear Schrödinger Cauchy problems.

Currently displaying 1 – 9 of 9