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For: Kapitula T, Kevrekidis PG, Malomed BA. Stability of multiple pulses in discrete systems. Phys Rev E Stat Nonlin Soft Matter Phys 2001;63:036604. [PMID: 11308785 DOI: 10.1103/physreve.63.036604] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/01/2000] [Indexed: 05/23/2023]
Number Cited by Other Article(s)
1
Malomed BA. Discrete and Semi-Discrete Multidimensional Solitons and Vortices: Established Results and Novel Findings. ENTROPY (BASEL, SWITZERLAND) 2024;26:137. [PMID: 38392392 PMCID: PMC10887582 DOI: 10.3390/e26020137] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/08/2024] [Revised: 01/26/2024] [Accepted: 01/28/2024] [Indexed: 02/24/2024]
2
Dutta O, Gajda M, Hauke P, Lewenstein M, Lühmann DS, Malomed BA, Sowiński T, Zakrzewski J. Non-standard Hubbard models in optical lattices: a review. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2015;78:066001. [PMID: 26023844 DOI: 10.1088/0034-4885/78/6/066001] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/28/2023]
3
Sakaguchi H, Kageyama Y. Modulational instability and breathing motion in the two-dimensional nonlinear Schrödinger equation with a one-dimensional harmonic potential. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013;88:053203. [PMID: 24329371 DOI: 10.1103/physreve.88.053203] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/25/2013] [Revised: 10/28/2013] [Indexed: 06/03/2023]
4
Malomed BA, Kaup DJ, Van Gorder RA. Unstaggered-staggered solitons in two-component discrete nonlinear Schrödinger lattices. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012;85:026604. [PMID: 22463346 DOI: 10.1103/physreve.85.026604] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/18/2011] [Indexed: 05/31/2023]
5
Barashenkov IV, Zemlyanaya EV. Soliton complexity in the damped-driven nonlinear Schrödinger equation: stationary to periodic to quasiperiodic complexes. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011;83:056610. [PMID: 21728685 DOI: 10.1103/physreve.83.056610] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/23/2010] [Revised: 02/07/2011] [Indexed: 05/31/2023]
6
Wang C, Theocharis G, Kevrekidis PG, Whitaker N, Law KJH, Frantzeskakis DJ, Malomed BA. Two-dimensional paradigm for symmetry breaking: the nonlinear Schrödinger equation with a four-well potential. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009;80:046611. [PMID: 19905475 DOI: 10.1103/physreve.80.046611] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/02/2009] [Revised: 08/27/2009] [Indexed: 05/28/2023]
7
Law KJH, Kevrekidis PG, Koukouloyannis V, Kourakis I, Frantzeskakis DJ, Bishop AR. Discrete solitons and vortices in hexagonal and honeycomb lattices: existence, stability, and dynamics. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008;78:066610. [PMID: 19256971 DOI: 10.1103/physreve.78.066610] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/28/2008] [Revised: 10/10/2008] [Indexed: 05/27/2023]
8
Leblond H, Malomed BA, Mihalache D. Three-dimensional vortex solitons in quasi-two-dimensional lattices. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007;76:026604. [PMID: 17930164 DOI: 10.1103/physreve.76.026604] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/12/2006] [Indexed: 05/25/2023]
9
Kevrekidis PG, Gagnon J, Frantzeskakis DJ, Malomed BA. X , Y , and Z waves: extended structures in nonlinear lattices. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007;75:016607. [PMID: 17358275 DOI: 10.1103/physreve.75.016607] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/14/2006] [Indexed: 05/14/2023]
10
Linzon Y, Sivan Y, Malomed B, Zaezjev M, Morandotti R, Bar-Ad S. Interaction-induced localization of anomalously diffracting nonlinear waves. PHYSICAL REVIEW LETTERS 2006;97:193901. [PMID: 17155629 DOI: 10.1103/physrevlett.97.193901] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/09/2006] [Indexed: 05/12/2023]
11
Gómez-Gardeñes J, Malomed BA, Floría LM, Bishop AR. Discrete solitons and vortices in the two-dimensional Salerno model with competing nonlinearities. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006;74:036607. [PMID: 17025764 DOI: 10.1103/physreve.74.036607] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/08/2006] [Indexed: 05/12/2023]
12
Gomez-Gardeñes J, Malomed BA, Floría LM, Bishop AR. Solitons in the Salerno model with competing nonlinearities. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006;73:036608. [PMID: 16605678 DOI: 10.1103/physreve.73.036608] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/21/2005] [Indexed: 05/08/2023]
13
Sakaguchi H, Malomed BA. Matter-wave solitons in nonlinear optical lattices. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005;72:046610. [PMID: 16383557 DOI: 10.1103/physreve.72.046610] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/19/2005] [Revised: 07/11/2005] [Indexed: 05/05/2023]
14
Susanto H, Johansson M. Discrete dark solitons with multiple holes. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005;72:016605. [PMID: 16090105 DOI: 10.1103/physreve.72.016605] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/28/2004] [Revised: 02/11/2005] [Indexed: 05/03/2023]
15
Carretero-González R, Kevrekidis PG, Malomed BA, Frantzeskakis DJ. Three-dimensional nonlinear lattices: from oblique vortices and octupoles to discrete diamonds and vortex cubes. PHYSICAL REVIEW LETTERS 2005;94:203901. [PMID: 16090247 DOI: 10.1103/physrevlett.94.203901] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/11/2005] [Indexed: 05/03/2023]
16
Kevrekidis PG, Khare A, Saxena A. Breather lattice and its stabilization for the modified Korteweg-de Vries equation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003;68:047701. [PMID: 14683090 DOI: 10.1103/physreve.68.047701] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/09/2003] [Indexed: 11/07/2022]
17
Domokos G, Holmes P. On nonlinear boundary-value problems: ghosts, parasites and discretizations. Proc Math Phys Eng Sci 2003. [DOI: 10.1098/rspa.2002.1091] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]  Open
18
Hudock J, Kevrekidis PG, Malomed BA, Christodoulides DN. Discrete vector solitons in two-dimensional nonlinear waveguide arrays: solutions, stability, and dynamics. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003;67:056618. [PMID: 12786307 DOI: 10.1103/physreve.67.056618] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/21/2001] [Revised: 01/23/2003] [Indexed: 05/24/2023]
19
Kevrekidis PG, Kivshar YS, Kovalev AS. Instabilities and bifurcations of nonlinear impurity modes. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003;67:046604. [PMID: 12786506 DOI: 10.1103/physreve.67.046604] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/16/2002] [Indexed: 05/24/2023]
20
Kevrekidis PG, Konotop VV, Bishop AR, Takeno S. Discrete compactons: some exact results. ACTA ACUST UNITED AC 2002. [DOI: 10.1088/0305-4470/35/45/103] [Citation(s) in RCA: 34] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
21
Kevrekidis PG, Kevrekidis IG, Bishop AR, Titi ES. Continuum approach to discreteness. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002;65:046613. [PMID: 12006053 DOI: 10.1103/physreve.65.046613] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/04/2001] [Indexed: 05/23/2023]
22
Sukhorukov AA, Kivshar YS. Spatial optical solitons in nonlinear photonic crystals. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002;65:036609. [PMID: 11909287 DOI: 10.1103/physreve.65.036609] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/06/2001] [Indexed: 05/23/2023]
23
Kevrekidis PG, Malomed BA, Bishop AR. Bound states of two-dimensional solitons in the discrete nonlinear Schrödinger equation. ACTA ACUST UNITED AC 2001. [DOI: 10.1088/0305-4470/34/45/302] [Citation(s) in RCA: 30] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
24
Skryabin DV. Energy of internal modes of nonlinear waves and complex frequencies due to symmetry breaking. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2001;64:055601. [PMID: 11736005 DOI: 10.1103/physreve.64.055601] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/14/2001] [Indexed: 05/23/2023]
25
Kevrekidis PG. Multipulses in discrete Hamiltonian nonlinear systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2001;64:026611. [PMID: 11497734 DOI: 10.1103/physreve.64.026611] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/19/2001] [Indexed: 05/23/2023]
26
Malomed BA, Kevrekidis PG. Discrete vortex solitons. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2001;64:026601. [PMID: 11497724 DOI: 10.1103/physreve.64.026601] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/12/2000] [Revised: 02/12/2001] [Indexed: 05/23/2023]
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