TITLE

Thick clusters for the radially symmetric nonlinear Schrödinger equation

AUTHOR(S)
Felmer, Patricio; Martínez, Salomé
PUB. DATE
February 2008
SOURCE
Calculus of Variations & Partial Differential Equations;Feb2008, Vol. 31 Issue 2, p231
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
This article is devoted to the study of radially symmetric solutions to the nonlinear Schrödinger equation where B is a ball in $${\mathbb{R}}^N$$ , 1 < p < ( N + 2)/( N − 2), N ≥ 3 and the potential V is radially symmetric. We construct positive clustering solutions in an annulus having O(1/ɛ) critical points, as well as sign changing solutions with O(1/ɛ) zeroes concentrating near zero.
ACCESSION #
27175311

 

Related Articles

  • Analysis and formation of acoustic fields in inhomogeneous waveguides. Gladkii, A.; Skopetskii, V.; Harrison, D. // Cybernetics & Systems Analysis;Mar2009, Vol. 45 Issue 2, p214 

    The problem of numerical modeling and formation of acoustic fields with definite properties in an axisymmetric inhomogeneous underwater waveguide is considered. A numerical method to solve a boundary-value and extremal problems for a parabolic Schrödinger-type wave equation with a complex...

  • ASYMPTOTIC BEHAVIOR FOR A QUADRATIC NONLINEAR SCHRÖDINGER EQUATION. HAYASHI, NAKAO; NAUMKIN, PAVEL I. // Electronic Journal of Differential Equations;2008, Vol. 2008, Special section p1 

    We study the initial-value problem for the quadratic nonlinear Schrödinger equation iut + 1/2 uxx = ∂xū², x ∈ ∇, t > 1, u(1, x) = u1(x), x ∈ ∇. For small initial data u1 ∈ H²,² we prove that there exists a unique global solution u ∈...

  • Solutions of Smooth Nonlinear Partial Differential Equations. van der Walt, Jan Harm // Abstract & Applied Analysis;2011, Special section p1 

    The method of order completion provides a general and type-independent theory for the existence and basic regularity of the solutions of large classes of systems of nonlinear partial differential equations (PDEs). Recently, the application of convergence spaces to this theory resulted in a...

  • WELL-POSEDNESS OF ONE-DIMENSIONAL KORTEWEG MODELS. Benzoni-Gavage, Sylvie; Danchin, Raphaël; Descombes, Stéphane // Electronic Journal of Differential Equations;2006, Vol. 2006, Special section p1 

    We investigate the initial-value problem for one-dimensional compressible fluids endowed with internal capillarity. We focus on the isothermal inviscid case with variable capillarity. The resulting equations for the density and the velocity, consisting of the mass conservation law and the...

  • Remarks on the Painlevé analysis for a (2+1)-dimensional generalization of nonlinear-Schrödinger-type equations. Zai-Chun Yang; Bo Tian // Journal of Mathematical Physics;Jul2007, Vol. 48 Issue 7, p073508 

    Choudhury [J. Math. Phys. 44, 5733 (2003)] applied truncated Painlevé expansions to derive Lax pairs, Darboux transformations, and various soliton solutions to some (2+1)-dimensional generalizations of nonlinear-Schrödinger-type equations, and the method he used was based on the techniques...

  • GENERALIZED, MASTER AND NONLOCAL SYMMETRIES OF CERTAIN DEFORMED NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS. SAHADEVAN, R.; NALINIDEVI, L. // Journal of Nonlinear Mathematical Physics (World Scientific Publ;Dec2010, Vol. 17 Issue 4, p517 

    It is shown that the deformed Nonlinear Schrödinger (NLS), Hirota and AKNS equations with (1 + 1) dimension admit infinitely many generalized (nonpoint) symmetries and polynomial conserved quantities, master symmetries and recursion operator ensuring their complete integrability. Also shown...

  • The direct algebraic method to complex nonlinear partial differential equations. Taghizadeh, N.; Mirzazadeh, M. // International Journal of Applied Mathematics & Computation;2013, Vol. 5 Issue 3, p12 

    By means of the two distinct methods, the direct algebraic method and the cosine method, we successfully performed an analytic study on the (2+1)-dimensional cubic nonlinear Schrödinger equation.

  • NODAL SOLUTIONS FOR A QUASILINEAR SCHRÖDINGER EQUATION WITH CRITICAL NONLINEARITY AND NON-SQUARE DIFFUSION. YINBIN DENG; YI LI; XIUJUAN YAN // Communications on Pure & Applied Analysis;Nov2015, Vol. 14 Issue 6, p2487 

    The article discusses the k-node solutions for quasilinear Schrödinger equation with critical nonlinearity and non-square diffusion. It mentions the different types of quasilinear Schrödinger equation. It notes that types of equations have been derived as models of several physical...

  • Modulation Instability, Breathers, and Bound Solitons in an Erbium-Doped Fiber System with Higher-Order Effects. Rui Guo; Hui-Qin Hao; Xiao-Song Gu // Abstract & Applied Analysis;2014, p1 

    We mainly investigate the generalized nonlinear Schrödinger-Maxwell-Bloch system which governs the propagation of optical solitons in nonlinear erbium-doped fibers with higher-order effects. We deduce Lax pair, analyze modulation instability conditions, construct the Darboux transformation,...

  • STABILIZATION OF SOLUTIONS TO HIGHER-ORDER NONLINEAR SCHRÖDINGER EQUATION WITH LOCALIZED DAMPING. Bisognin, Eleni; Bisognin, Vanilde; Villagrán, Octavio Paulo Vera // Electronic Journal of Differential Equations;2007, Vol. 2007, p1 

    We study the stabilization of solutions to higher-order nonlinear Schrödinger equations in a bounded interval under the effect of a localized damping mechanism. We use multiplier techniques to obtain exponential decay in time of the solutions of the linear and nonlinear equations.

Share

Read the Article

Courtesy of VIRGINIA BEACH PUBLIC LIBRARY AND SYSTEM

Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics