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Volumn 226, Issue 2, 2007, Pages 1693-1709

A mode elimination technique to improve convergence of iteration methods for finding solitary waves

Author keywords

Convergence acceleration; Iteration methods; Nonlinear evolution equations; Solitary waves

Indexed keywords

ACCELERATION; CONTROL NONLINEARITIES; ITERATIVE METHODS; NONLINEAR EQUATIONS;

EID: 34548692072     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2007.06.010     Document Type: Article
Times cited : (27)

References (14)
  • 1
    • 85190293611 scopus 로고    scopus 로고
    • T.I. Lakoba, J. Yang, A generalized Petviashvili iteration method for scalar and vector Hamiltonian equations with arbitrary form of nonlinearity, J. Comput. Phys., this issue, doi:10.1016/j.jcp.2007.06.009.
  • 2
    • 0038402861 scopus 로고
    • Equation for an extraordinary soliton
    • Petviashvili V.I. Equation for an extraordinary soliton. Sov. J. Plasma Phys. 2 (1976) 257-258
    • (1976) Sov. J. Plasma Phys. , vol.2 , pp. 257-258
    • Petviashvili, V.I.1
  • 3
    • 0036344565 scopus 로고    scopus 로고
    • Optimizing Schrödinger functionals using Sobolev gradients: applications to quantum mechanics and nonlinear optics
    • Garcia-Ripoll J.J., and Perez-Garcia V.M. Optimizing Schrödinger functionals using Sobolev gradients: applications to quantum mechanics and nonlinear optics. SIAM J. Sci. Comput. 23 (2001) 1316-1334
    • (2001) SIAM J. Sci. Comput. , vol.23 , pp. 1316-1334
    • Garcia-Ripoll, J.J.1    Perez-Garcia, V.M.2
  • 4
    • 6344289363 scopus 로고    scopus 로고
    • Computing the ground state solution of Bose-Einstein condensates by a normalized gradient flow
    • Bao W., and Du Q. Computing the ground state solution of Bose-Einstein condensates by a normalized gradient flow. SIAM J. Sci. Comput. 25 (2004) 1674-1697
    • (2004) SIAM J. Sci. Comput. , vol.25 , pp. 1674-1697
    • Bao, W.1    Du, Q.2
  • 5
    • 85190237160 scopus 로고    scopus 로고
    • V.S. Shchesnovich, S.B. Cavalcanti, Rayleigh functional for nonlinear systems. Available from: (preprint nlin.PS/0411033).
  • 6
    • 85190285375 scopus 로고    scopus 로고
    • J. Yang, T.I. Lakoba, Convergence and acceleration of imaginary-time evolution methods for solitary waves in arbitrary spatial dimensions, submitted.
  • 7
    • 21244436462 scopus 로고    scopus 로고
    • Convergence of Petviashvili's iteration method for numerical approximation of stationary solutions of nonlinear wave equations
    • Pelinovsky D.E., and Stepanyants Yu.A. Convergence of Petviashvili's iteration method for numerical approximation of stationary solutions of nonlinear wave equations. SIAM J. Numer. Anal. 42 (2004) 1110-1127
    • (2004) SIAM J. Numer. Anal. , vol.42 , pp. 1110-1127
    • Pelinovsky, D.E.1    Stepanyants, Yu.A.2
  • 8
    • 33845976330 scopus 로고    scopus 로고
    • Universally-convergent squared-operator iteration methods for solitary waves in general nonlinear wave equations
    • Yang J., and Lakoba T. Universally-convergent squared-operator iteration methods for solitary waves in general nonlinear wave equations. Stud. Appl. Math. 118 (2007) 153-197
    • (2007) Stud. Appl. Math. , vol.118 , pp. 153-197
    • Yang, J.1    Lakoba, T.2
  • 9
    • 27844572414 scopus 로고    scopus 로고
    • Differential equations and solution of linear systems
    • Chehab J.-P., and Laminie J. Differential equations and solution of linear systems. Numer. Algorithms 40 (2005) 103-124
    • (2005) Numer. Algorithms , vol.40 , pp. 103-124
    • Chehab, J.-P.1    Laminie, J.2
  • 10
    • 0000585502 scopus 로고
    • Two-dimensional solitons of the Kadomtsev-Petviashvili equation and their interaction
    • Manakov S.V., Zakharov V.E., Bordag L.A., Its A.R., and Matveev V.B. Two-dimensional solitons of the Kadomtsev-Petviashvili equation and their interaction. Phys. Lett. A 63 (1977) 205
    • (1977) Phys. Lett. A , vol.63 , pp. 205
    • Manakov, S.V.1    Zakharov, V.E.2    Bordag, L.A.3    Its, A.R.4    Matveev, V.B.5
  • 11
    • 84990553584 scopus 로고
    • Lyapunov stability of ground states of nonlinear dispersive evolution equations
    • Weinstein M. Lyapunov stability of ground states of nonlinear dispersive evolution equations. Comm. Pure Appl. Math. 39 (1986) 51-67
    • (1986) Comm. Pure Appl. Math. , vol.39 , pp. 51-67
    • Weinstein, M.1
  • 12
    • 0004151494 scopus 로고
    • Cambridge University Press, New York
    • Horn R., and Johnson C. Matrix Analysis (1991), Cambridge University Press, New York
    • (1991) Matrix Analysis
    • Horn, R.1    Johnson, C.2
  • 13
    • 0004045886 scopus 로고
    • Addison-Wesley Publishing Co., Reading Problem 8 for Section 4.3.2
    • Johnson L.W., and Riess R.D. Numerical Analysis (1977), Addison-Wesley Publishing Co., Reading Problem 8 for Section 4.3.2
    • (1977) Numerical Analysis
    • Johnson, L.W.1    Riess, R.D.2
  • 14
    • 33645070786 scopus 로고    scopus 로고
    • Numerical verification of a gap condition for a linearized nonlinear Schrödinger equation
    • Demanet L., and Schlag W. Numerical verification of a gap condition for a linearized nonlinear Schrödinger equation. Nonlinearity 19 (2006) 829-852
    • (2006) Nonlinearity , vol.19 , pp. 829-852
    • Demanet, L.1    Schlag, W.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.