MASS CONCENTRATION WITH MIXED NORM FOR A NONELLIPTIC SCHRÖDINGER EQUATION

AbstractThis paper is concerned with a mass concentration phenomenon for a two-dimensional nonelliptic Schrödinger equation. It is well known that this phenomenon occurs when the ${L}^{4} $-norm of the solution blows up in finite time. We extend this result to the case where a mixed norm of the solution blows up in finite time.

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``Mass concentration'' phenomenon for the nonlinear Schrödinger equation with the critical power nonlinearity. II.

Kodai Mathematical Journal ◽

10.2996/kmj/1138039278 ◽

1990 ◽

Vol 13 (3) ◽

pp. 333-348 ◽

Cited By ~ 10

Author(s):

Hayato Nawa

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Mass Concentration ◽

Critical Power ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger ◽

Power Nonlinearity ◽

Concentration Phenomenon

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Mass Concentration Phenomenon for the Quintic Nonlinear Schrödinger Equation in One Dimension

SIAM Journal on Mathematical Analysis ◽

10.1137/050626284 ◽

2006 ◽

Vol 37 (6) ◽

pp. 1923-1946 ◽

Cited By ~ 7

Author(s):

Nikolaos Tzirakis

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Mass Concentration ◽

Nonlinear Schrodinger Equation ◽

One Dimension ◽

Nonlinear Schrödinger ◽

Quintic Nonlinear Schrödinger Equation ◽

Concentration Phenomenon

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Local well-posedness for the quadratic Schrödinger equation in two-dimensional compact manifolds with boundary

São Paulo Journal of Mathematical Sciences ◽

10.1007/s40863-021-00249-w ◽

2021 ◽

Author(s):

Marcelo Nogueira ◽

Mahendra Panthee

Keyword(s):

Schrödinger Equation ◽

Schrodinger Equation ◽

Compact Manifolds ◽

Well Posedness ◽

Two Dimensional ◽

Manifolds With Boundary

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Local absorbing boundary conditions for two‐dimensional nonlinear Schrödinger equation with wave operator on unbounded domain

Mathematical Methods in the Applied Sciences ◽

10.1002/mma.7703 ◽

2021 ◽

Author(s):

Hongwei Li

Keyword(s):

Schrödinger Equation ◽

Boundary Conditions ◽

Nonlinear Schrödinger Equation ◽

Unbounded Domain ◽

Wave Operator ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Absorbing Boundary Conditions ◽

Two Dimensional ◽

Absorbing Boundary

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Stability of one and two-dimensional spatial solitons in a cubic-quintic-septimal nonlinear Schrödinger equation with fourth-order diffraction and PT-symmetric potentials

Wave Motion ◽

10.1016/j.wavemoti.2021.102810 ◽

2021 ◽

pp. 102810

Author(s):

Boubakary Abdou ◽

Fabien II Ndzana ◽

Latchio Tiofack Gaston ◽

Alidou Mohamadou

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Fourth Order ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Two Dimensional ◽

Spatial Solitons ◽

Nonlinear Schrödinger ◽

Order Diffraction

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Simple multiple explode–decay mode solutions of a two‐dimensional nonlinear Schrödinger equation

Journal of Mathematical Physics ◽

10.1063/1.525361 ◽

1982 ◽

Vol 23 (3) ◽

pp. 417-420 ◽

Cited By ~ 9

Author(s):

Akira Nakamura

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Decay Mode ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Two Dimensional ◽

Nonlinear Schrödinger

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Blow-up rate, mass concentration and asymptotic profile of blow-up solutions for the nonlinear inhomogeneous Schrödinger equation

Applied Mathematics and Computation ◽

10.1016/j.amc.2014.06.061 ◽

2014 ◽

Vol 242 ◽

pp. 889-897

Author(s):

Shihui Zhu ◽

Han Yang ◽

Jian Zhang

Keyword(s):

Schrödinger Equation ◽

Schrodinger Equation ◽

Mass Concentration ◽

Blow Up ◽

Asymptotic Profile ◽

Blow Up Rate ◽

Inhomogeneous Schrödinger Equation

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A Dynamic Adaptive Wavelet Method for Solution of the Schrodinger Equation

Journal of Multiscale Modelling ◽

10.1142/s1756973714500012 ◽

2015 ◽

Vol 06 (01) ◽

pp. 1450001 ◽

Cited By ~ 2

Author(s):

Ratikanta Behera ◽

Mani Mehra

Keyword(s):

Schrödinger Equation ◽

Computational Efficiency ◽

Schrodinger Equation ◽

Computational Cost ◽

Two Dimensional ◽

Wavelet Method ◽

Adaptive Wavelet ◽

One Dimensional ◽

Grid Adaptation ◽

Adaptive Wavelet Method

In this paper, we present a dynamically adaptive wavelet method for solving Schrodinger equation on one-dimensional, two-dimensional and on the sphere. Solving one-dimensional and two-dimensional Schrodinger equations are based on Daubechies wavelet with finite difference method on an arbitrary grid, and for spherical Schrodinger equation is based on spherical wavelet over an optimal spherical geodesic grid. The method is applied to the solution of Schrodinger equation for computational efficiency and achieve accuracy with controlling spatial grid adaptation — high resolution computations are performed only in regions where a solution varies greatly (i.e., near steep gradients, or near-singularities) and a much coarser grid where the solution varies slowly. Thereupon the dynamic adaptive wavelet method is useful to analyze local structure of solution with very less number of computational cost than any other methods. The prowess and computational efficiency of the adaptive wavelet method is demonstrated for the solution of Schrodinger equation on one-dimensional, two-dimensional and on the sphere.

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