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Volumn 6, Issue 1, 2006, Pages 151-167

Traveling waves in compressible elastic rods

Author keywords

Elasticity; Nonlinear wave equations; Traveling waves

Indexed keywords


EID: 33644539555     PISSN: 15313492     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcdsb.2006.6.151     Document Type: Article
Times cited : (21)

References (26)
  • 1
    • 0000174121 scopus 로고    scopus 로고
    • Acoustic scattering and the extended korteweg-de vries hierarchy
    • R. Beals, D. Sattinger, and J. Szmigielski, Acoustic scattering and the extended Korteweg-de Vries hierarchy, Adv. Math., 40 (1998), 190-206.
    • (1998) Adv. Math. , vol.40 , pp. 190-206
    • Beals, R.1    Sattinger, D.2    Szmigielski, J.3
  • 2
    • 0001865962 scopus 로고
    • Model equations for long waves in nonlinear dispersive systems
    • London
    • B. Benjamin, J. Bona, and J. Mahony, Model equations for long waves in nonlinear dispersive systems, Phil. Trans. R. Soc. London, 272 (1972), 47-78.
    • (1972) Phil. Trans. R. Soc. , vol.272 , pp. 47-78
    • Benjamin, B.1    Bona, J.2    Mahony, J.3
  • 3
    • 0001767796 scopus 로고
    • An evaluation of a model equation for water waves
    • J. Bona, W. Pritchard, and L. Scott, An evaluation of a model equation for water waves, Phil. Trans. R. Soc. London, 302 (1981), 457-510.
    • (1981) Phil. Trans. R. Soc. London , vol.302 , pp. 457-510
    • Bona, J.1    Pritchard, W.2    Scott, L.3
  • 4
    • 0001610690 scopus 로고
    • Numerical schemes for a model for nonlinear dispersive waves
    • J. Bona, W. Pritchard, and L. Scott, Numerical schemes for a model for nonlinear dispersive waves, J. Comput. Phys., 60 (1985), 167-186.
    • (1985) J. Comput. Phys. , vol.60 , pp. 167-186
    • Bona, J.1    Pritchard, W.2    Scott, L.3
  • 5
    • 12044254491 scopus 로고
    • An integrable shallow water equation with peaked solitons
    • R. Camassa and D. Holm, An integrable shallow water equation with peaked solitons, Phys. Rev. Lett., 71 (1993), 1661-1664.
    • (1993) Phys. Rev. Lett. , vol.71 , pp. 1661-1664
    • Camassa, R.1    Holm, D.2
  • 6
    • 0034415062 scopus 로고    scopus 로고
    • Existence of permanent and breaking waves for a shallow water equation: A geometric approach
    • A. Constantin, Existence of permanent and breaking waves for a shallow water equation: a geometric approach, Ann. Inst. Fourier (Grenoble), 50 (2000), 321-362.
    • (2000) Ann. Inst. Fourier (Grenoble) , vol.50 , pp. 321-362
    • Constantin, A.1
  • 7
    • 34447130573 scopus 로고    scopus 로고
    • On the scattering problem for the camassa-holm equation
    • London
    • A. Constantin, On the scattering problem for the Camassa-Holm equation, Proc. Roy. Soc. London, 457 (2001), 953-970.
    • (2001) Proc. Roy. Soc. , vol.457 , pp. 953-970
    • Constantin, A.1
  • 8
    • 0000985293 scopus 로고    scopus 로고
    • Wave breaking for nonlinear nonlocal shallow water equations
    • A. Constantin and J. Escher, Wave breaking for nonlinear nonlocal shallow water equations, Acta Mathematica, 181 (1998), 229-243.
    • (1998) Acta Mathematica , vol.181 , pp. 229-243
    • Constantin, A.1    Escher, J.2
  • 9
    • 0042279206 scopus 로고    scopus 로고
    • On the geometric approach to the motion of inertial mechanical systems
    • A. Constantin and B. Kolev, On the geometric approach to the motion of inertial mechanical systems, J. Phys. A, 35 (2002), R51-R79.
    • (2002) J. Phys. A , vol.35
    • Constantin, A.1    Kolev, B.2
  • 10
    • 0242350978 scopus 로고    scopus 로고
    • Geodesic flow on the diffeomorphism group of the circle
    • A. Constantin and B. Kolev, Geodesic flow on the diffeomorphism group of the circle, Comment. Math. Helv., 78 (2003), 787-804.
    • (2003) Comment. Math. Helv. , vol.78 , pp. 787-804
    • Constantin, A.1    Kolev, B.2
  • 11
    • 0033415933 scopus 로고    scopus 로고
    • A shallow water equation on the circle
    • A. Constantin and H. P. McKean, A shallow water equation on the circle, Comm. Pure Appl. Math., 52 (1999), 949-982.
    • (1999) Comm. Pure Appl. Math. , vol.52 , pp. 949-982
    • Constantin, A.1    McKean, H.P.2
  • 13
    • 0034729052 scopus 로고    scopus 로고
    • Stability of a class of solitary waves in compressible elastic rods
    • A. Constantin and W. Strauss, Stability of a class of solitary waves in compressible elastic rods, Phys. Lett. A, 270 (2000), 140-148.
    • (2000) Phys. Lett. A , vol.270 , pp. 140-148
    • Constantin, A.1    Strauss, W.2
  • 14
    • 0000380413 scopus 로고    scopus 로고
    • Stability of the camassa-holm solitons
    • A. Constantin and W. Strauss, Stability of the Camassa-Holm solitons, J. Nonlinear Sci., 12 (2002), 415-422.
    • (2002) J. Nonlinear Sci. , vol.12 , pp. 415-422
    • Constantin, A.1    Strauss, W.2
  • 15
    • 0031679566 scopus 로고    scopus 로고
    • Model equations for nonlinear dispersive waves in a compressible mooney-rivlin rod
    • H.-H. Dai, Model equations for nonlinear dispersive waves in a compressible Mooney-Rivlin rod, Acta Mech., 127 (1998), 193-207.
    • (1998) Acta Mech. , vol.127 , pp. 193-207
    • Dai, H.-H.1
  • 16
    • 0000171588 scopus 로고    scopus 로고
    • Solitary shock waves and other travelling waves in a general compressible hyperelastic rod
    • H.-H. Dai and Y. Huo, Solitary shock waves and other travelling waves in a general compressible hyperelastic rod, Proc. R. Soc. Lond. A, 456 (2000), 331-363.
    • (2000) Proc. R. Soc. Lond. A , vol.456 , pp. 331-363
    • Dai, H.-H.1    Huo, Y.2
  • 17
    • 49049150360 scopus 로고
    • Symplectic structures, their Bäcklund transformation and hereditary symmetries
    • A. Fokas and B. Fuchssteiner, Symplectic structures, their Bäcklund transformation and hereditary symmetries, Physica D, 4 (1981), 47-66.
    • (1981) Physica D , vol.4 , pp. 47-66
    • Fokas, A.1    Fuchssteiner, B.2
  • 19
    • 0037171407 scopus 로고    scopus 로고
    • Camassa-Holm, Korteweg-de Vries and related models for water waves
    • R. Johnson, Camassa-Holm, Korteweg-de Vries and related models for water waves, J. Fluid Mech., 455 (2002), 63-82.
    • (2002) J. Fluid Mech. , vol.455 , pp. 63-82
    • Johnson, R.1
  • 20
    • 13544277180 scopus 로고    scopus 로고
    • Numerical study of traveling-wave solutions for the camassa-holm equation
    • H. Kalisch and J. Lenells, Numerical study of traveling-wave solutions for the Camassa-Holm equation, Chaos, Solitons and Fractals, 25 (2005), 287-298.
    • (2005) Chaos, Solitons and Fractals , vol.25 , pp. 287-298
    • Kalisch, H.1    Lenells, J.2
  • 21
    • 0036434830 scopus 로고    scopus 로고
    • The scattering approach for the camassa-holm equation
    • Lenells J, The scattering approach for the Camassa-Holm equation, J. Nonlinear Math. Phys., 9 (2002), 389-393.
    • (2002) J. Nonlinear Math. Phys. , vol.9 , pp. 389-393
    • Lenells, J.1
  • 22
    • 1342267624 scopus 로고    scopus 로고
    • Stability of periodic peakons
    • J. Lenells, Stability of periodic peakons, Internat. Math. Res. Notices, 10 (2004), 485-499.
    • (2004) Internat. Math. Res. Notices , vol.10 , pp. 485-499
    • Lenells, J.1
  • 23
    • 2442664231 scopus 로고    scopus 로고
    • A variational approach to the stability of periodic peakons
    • J. Lenells, A variational approach to the stability of periodic peakons, J. Nonlinear Math. Phys., 11 (2004), 151-163.
    • (2004) J. Nonlinear Math. Phys. , vol.11 , pp. 151-163
    • Lenells, J.1
  • 24
    • 13544258272 scopus 로고    scopus 로고
    • Traveling wave solutions of the camassa-holm equation
    • to appear
    • J. Lenells, Traveling wave solutions of the Camassa-Holm equation, J. Diff. Eq., to appear.
    • J. Diff. Eq.
    • Lenells, J.1
  • 25
    • 0031989845 scopus 로고    scopus 로고
    • A shallow water equation as a geodesic flow on the bott-virasoro group
    • G. Misiolek, A shallow water equation as a geodesic flow on the Bott-Virasoro group, J. Geom. Phys., 24 (1998), 203-208.
    • (1998) J. Geom. Phys. , vol.24 , pp. 203-208
    • Misiolek, G.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.