By Ambrosetti A., Colorado E., Ruiz D.
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Additional resources for Multi-bump solitons to linearly coupled systems of nonlinear Schrödinger equations
Pisa Cl. Sci. (4) 27 (1998), 331–377 (1999). 42  S. Cingolani, M. Nolasco, Multi-peak periodic semiclassical states for a class of nonlinear Schr¨ odinger equations, Proc. Royal Soc. A, 128 (1998), 1249-1260. M. Coxeter, Regular polytopes, Methuen & Co. , London, 1948.  A. Floer, A. Weinstein, Nonspreading wave packets for the cubic Schr¨ odinger equation with a bounded potential, J. Funct. 69 (1986), 397-408.  X. Kang, J. Wei, On interacting bumps of semi-classical states of nonlinear Schr¨ odinger equations, Adv.
10) is above a fixed positive constant. 3 In the previous sections we have proved that (A1) and (A2) hold. 9). So, we are led with the study of critical points of the reduced functional, that is, the function: Φ (ξ) = Φ (z ,ξ + w ,ξ ). 6. 10 There exist positive constants C , C, C > 0 such that Φ (ξ) = C − a ,ξ |ξ| 1−n 2 e−sξ + b |ξ| ,ξ where C is independent of ξ and a ,ξ , 3−n 2 b ,ξ e−rξ + o( s s−r ), ∀ξ ∈ T , ∼ 0, ∈ [C, C]. Proof. To simplify notation we will write z instead of z ,ξ and w instead of w ,ξ .
Phys, 131 (1990), 223-253. S. Palais, The principle of symmetric criticality, Comm. Math. Phys. 69 (1979), 19-30.  A. Pomponio, Coupled nonlinear Schr¨ odinger systems with potentials, To appear in Jour. Diff. Eqns. 2006.  B. Sirakov, Least energy solitary waves for a system of nonlinear Schr¨ odinger equations in Rn , preprint.  M. Willem, Minimax theorems, Progress in Nonlinear Differential Equations and Their Applications, 24, Birk¨auser Boston, MA, 1996.
Multi-bump solitons to linearly coupled systems of nonlinear Schrödinger equations by Ambrosetti A., Colorado E., Ruiz D.