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tional methods, for a system of weakly coupled nonlinear Schrödinger equations. The main goal is to obtain a positive solution, of minimal ac- tion if possible.
Table of contents

International Mathematics Research Notices. Journal of Nonlinear Science 26 :6, Calculus of Variations and Partial Differential Equations 55 Discrete and Continuous Dynamical Systems 37 :4, Communications on Pure and Applied Mathematics 69 :9, Discrete and Continuous Dynamical Systems 36 , Communications in Mathematical Physics :1, Archive for Rational Mechanics and Analysis :2, Physica D: Nonlinear Phenomena , Archive for Rational Mechanics and Analysis.

Discrete and Continuous Dynamical Systems 36 :7, Journal of Nonlinear Science 26 :1, Nonlinearity 29 :1, Discrete and Continuous Dynamical Systems 36 :6, Proceedings of the London Mathematical Society :2, Communications in Contemporary Mathematics 17 , Nonlinearity 28 :3, Communications on Pure and Applied Analysis 14 :3, Journal of Differential Equations :3, Dynamics of Partial Differential Equations, Journal of Differential Equations , Communications in Partial Differential Equations 39 :8, Applicable Analysis 93 :8, Forum of Mathematics, Sigma 2.

Journal of the London Mathematical Society 89 :2, I: Dynamics near the soliton. Acta Mathematica :1, Mathematical Models and Methods in Applied Sciences 24 , Communications in Mathematical Physics :3, Communications in Partial Differential Equations 39 :1, Journal of Mathematical Physics 55 :1, Variational Methods in Nonlinear Field Equations, Physical Review B 88 Discrete and Continuous Dynamical Systems 34 :5, Journal of Functional Analysis :6, Journal of Nonlinear Science 23 :4, Acta Mathematica :2, Journal of Mathematical Physics 54 :6, Russian Mathematical Surveys 68 :2, Numerische Mathematik :3, Orbital Stability of Waves in Hamiltonian Systems.

Advanced Nonlinear Studies

Spectral and Dynamical Stability of Nonlinear Waves, Discrete and Continuous Dynamical Systems 33 :6, Journal of Physics A: Mathematical and Theoretical 45 , Physical Review A 86 Nonlinearity 25 :8, Journal of Functional Analysis :2, Mathematische Annalen :3, Communications in Partial Differential Equations 37 :6, Calculus of Variations and Partial Differential Equations 44 , Communications on Pure and Applied Mathematics 65 :4, Archive for Rational Mechanics and Analysis :3, Journal of Mathematical Physics 53 :3, Science China Mathematics 55 :2, Communications in Nonlinear Science and Numerical Simulation 17 :2, Physica D: Nonlinear Phenomena :2, Nonlinearity 25 :1, Mathematical Modelling of Natural Phenomena 7 :2, Inventiones mathematicae :1, Journal of Mathematical Physics 52 , Communications on Pure and Applied Analysis 11 :2, Nonlinearity 24 , Annals of Mathematics :2, Nonlinearity 24 :9, Journal of Mathematical Physics 52 :8, Communications in Mathematical Physics :2, Journal of Functional Analysis :1, Discrete and Continuous Dynamical Systems 31 :1, Discrete and Continuous Dynamical Systems 30 :4, Journal of Mathematical Physics 52 :3, Optics Letters 36 :3, Nonlinearity 24 :2, Communications in Partial Differential Equations 36 :3, Canadian Mathematical Bulletin 53 :4, Journal of Computational Physics , Geometric and Functional Analysis 20 :4, SeMA Journal 52 :1, Nonlinearity 23 :9, Journal of Nonlinear Science 20 :4, Physical Review A 81 Mathematical Modelling of Natural Phenomena 5 :4, Annals of Mathematics :1, Nonlinearity 23 :1, Journal of Mathematical Physics 51 :3, Visions in Mathematics, Communications on Pure and Applied Mathematics 62 , Reviews in Mathematical Physics 21 , Nonlinearity 22 :4, Physica D: Nonlinear Phenomena :1, Physical Review E 78 Physical Review A 78 Physica D: Nonlinear Phenomena :8, Mathematische Annalen :2, Physical Review E 77 Nonlinearity 21 :3, Journal of Mathematical Physics 49 :3, The case of the KdV equation.

Journal of Computational Physics :3, Nonlinearity 20 :5, Nonlinearity 20 :4, Journal of Differential Equations :1, Journal of the London Mathematical Society 75 :1, Journal of Computational Physics :1, Reviews in Mathematical Physics 18 , Journal of Mathematical Physics 47 :7, Communications on Pure and Applied Mathematics 59 :6, Journal of the Optical Society of America B 23 :4, Nonlinearity 19 :4, Russian Journal of Mathematical Physics 13 :2, SIAM Review 48 :4, Extended Hamiltonian Systems.

Thus, by 2. Therefore the proof of the lemma is completed. Hence, by 2. Moreover, by the Sobolev embedding theorem, we have. In this section, we study the existence of radially positive least energy solutions to 1. To prove the theorem, we set. Then 3. We deduce from the second equation of system 3.

Positive solutions for Schrödinger system with asymptotically periodic potentials

Note that. Then, by the second equation of 3.

Then we have. It follows from 3. By Lemmas 3.


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Moreover, by F 1 , F 3 we see that. Similarly to the proof of 3.

The Nonlinear Schroedinger Equation (NLSE) with a Random Potential... - Shmuel Fishman

Hence, by the second equation of 3. Then, by the first equation of 3. So we have. It contradicts 2. So by 3.


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