Nonlinear Schrödinger equations
Multiple solutions to nonlinear Schrödinger equations with critical growth
... Full list of author information is available at the end of the article Abstract In 2000, Cingolani and Lazzo (J. Differ. Equ. 160:118-138, 2000) studied nonlinear Schrödinger equations with competing ...
20
Computational Methods for Three Coupled Nonlinear Schrödinger Equations
... M. S. Ismail, S. H. Alaseri Department of Math, King Abdulaziz University, Jeddah, Kingdom of Saudi Arabia Abstract In this work, we will derive numerical schemes for solving 3-coupled nonlinear Schrödinger ...
23
Radial sign-changing solutions to biharmonic nonlinear Schrödinger equations
... 2. Rabinowitz, PH: On a class of nonlinear Schrödinger equations. Z. Angew. Math. Phys. 43, 270-291 (1992) 3. Wang, X: On concentration of positive bound states of nonlinear Schrödinger ...
17
Several conservative compact schemes for a class of nonlinear Schrödinger equations with wave operator
... In this paper, several different conserving compact finite difference schemes are developed for solving a class of nonlinear Schrödinger equations with wave operator. It is proved that the numerical ...
17
Blow-up for the stochastic nonlinear Schrödinger equations with quadratic potential and additive noise
... Abstract We study the dynamics of a stochastic nonlinear Schrödinger equation with both a quadratic potential and an additive noise. We show that in both cases of repulsive potential and attractive one, any ...
18
Ground state solutions for periodic discrete nonlinear Schrödinger equations with saturable nonlinearities
... discrete nonlinear Schrödinger equations with superlinear ...discrete nonlinear Schrödinger ...discrete nonlinear Schrödinger ...
13
Exact Travelling Wave Solutions of Two Nonlinear Schrödinger Equations by Using Two Methods
... Cubic-quintic nonlinear Schrödinger equation and the generalized nonlinear Schrödinger equation are studied by using the two ...two nonlinear Schrödinger equations are ...
15
Asymptotic expansion of small analytic solutions to the quadratic nonlinear Schrödinger equations in two dimensional spaces
... the nonlinear Schrödinger equa- tions were studied extensively in the case of the nonlinear terms without derivatives of unknown function and satisfying the gauge condition ...derivative ...
16
Lie Symmetries, One Dimensional Optimal System and Optimal Reduction of (2 + 1) Coupled nonlinear Schrödinger Equations
... [10] Nakamura, A. (1982) Simple Multiple Explode-Decay Mode Solutions of a Two-Dimensional Nonlinear Schrödinger Equation. Journal of Mathematical Physics, 23, 417. http://dx.doi.org/10.1063/1.525361 [11] ...
15
The existence and stability of solitons in discrete nonlinear Schrödinger equations
... 1.4.4.2 Perturbation expansions These methods are used to approximate solutions of a system, which is not explicitly solvable, in a small range of parameter values. As ‘small’ is relative, we first need to ...
178
Solutions of the Vector Nonlinear Schrödinger Equations: Evidence for Deterministic Rogue Waves
... 2 INFN, ‘‘Sapienza’’ Universita` di Roma, P.le A. Moro 2, 00185 Rome, Italy (Received 2 April 2012; published 26 July 2012) We construct and discuss a semirational, multiparametric vector solution of coupled ...
5
Chirped Peregrine solitons in a class of cubic-quintic nonlinear Schrödinger equations
... cubic-quintic nonlinear Schr¨odinger ...self-defocusing nonlinear medium may be attributed to the presence of self-steepening effect when the latter is not balanced out by the third-order ...
8
INFINITELY MANY SOLUTIONS FOR CUBIC NONLINEAR SCHRÖDINGER EQUATIONS IN DIMENSION FOUR
... ODINGER EQUATIONS IN DIMENSION FOUR J ´ ER ˆ OME V ´ ETOIS AND SHAODONG WANG ...cubic nonlinear Schr¨ odinger equations in the optimal dimension ...
14
Exact Solutions of two-Dimensional Nonlinear Schrödinger Equations with External Potentials
... Solitons are localized nonlinear waves and occur in many branches of physics. Their properties have provided fundamental understanding of complex nonlinear systems. In recent years there has been ...
7
Modulational instability of bright solitary waves in incoherently coupled nonlinear Schrödinger equations
... VII. SUMMARY We have analyzed and described dispersive MI of fam- ilies of nodeless spatial solitons in the system of the two incoherently coupled NLS equations. Considering cou- pled soliton states, we have ...
12
Existence of the global attractor to fractional order generalized coupled nonlinear Schrödinger equations with derivative
... In this paper, we are concerned with the fractional Schrödinger equation with time fraction order, fractional Laplacian, and derivative terms. The existence of weak solution is established, as well as the ...
27
Multiple soliton solutions and a generalized double Wronskian determinant to the \((2+1)\) dimensional nonlinear Schrödinger equations
... 4. Zhu, HJ, Chen, YM, Song, SH, Hu, HY: Symplectic and multi-symplectic wavelet collocation methods for two-dimensional Schrödinger equations. Appl. Numer. Math. 61(3), 308-321 (2011) 5. Malomed, B, Torner, ...
10
Gibbs measures of nonlinear Schrödinger equations as limits of quantum many body states in dimensions d <=3
... Abstract We prove that Gibbs measures of nonlinear Schr¨ odinger equations arise as high-temperature limits of thermal states in many-body quantum mechanics. Our results hold for defocusing inter- actions ...
97
Perfectly Matched Layer for computing the dynamics of nonlinear Schrödinger equations by pseudospectral methods. Application to rotating Bose-Einstein condensates
... the nonlinear Schr¨ odinger equation, e.g. in quantum optics or nonlinear wave propagation), the condensate ...the nonlinear Schr¨ odinger equation, considering that the wave function propagates out ...
19
On the Stability of the Defocusing Mass Critical Nonlinear Schrödinger Equation
... described nonlinear Schrödinger equations in exterior ...energy-critical nonlinear Schrödinger equation and the focusing cubic nonlinear Schrödinger equation in the ...
7