메뉴 건너뛰기




Volumn 461, Issue 2063, 2005, Pages 3611-3632

On the Camassa-Holm equation and a direct method of solution. II. soliton solutions

Author keywords

Bilinear form; Camassa holm equation; Multipeakons; Solitons

Indexed keywords

BILINEAR FORM; BILINEAR TRANSFORMATION; CAMASSA-HOLM EQUATION; CAMASSA-HOLM EQUATIONS; DIRECT METHOD; KEY PARAMETERS; MULTIPEAKONS; MULTISOLITON SOLUTIONS; N-SOLITON SOLUTIONS; PARAMETER REGIMES; SOLITARY WAVE SOLUTION; SOLITON SOLUTIONS; STRUCTURE AND DYNAMICS; TWO SOLITON SOLUTIONS;

EID: 28544450796     PISSN: 13645021     EISSN: 14712946     Source Type: Journal    
DOI: 10.1098/rspa.2005.1536     Document Type: Article
Times cited : (62)

References (26)
  • 2
    • 0016369301 scopus 로고
    • The inverse scattering transform-Fourier analysis for nonlinear problems
    • Ablowitz, M. J., Kaup, D. J., Newell, A. C. and Segur, H. 1974 The inverse scattering transform-Fourier analysis for nonlinear problems. Stud. Appl. Math. 53, 249-315.
    • (1974) Stud. Appl. Math , vol.53 , pp. 249-315
    • Ablowitz, M.J.1    Kaup, D.J.2    Newell, A.C.3    Segur, H.4
  • 3
    • 0000174121 scopus 로고    scopus 로고
    • Acoustic scattering and the extended Korteweg-de Vries hierarchy
    • doi:10.1006/aima.1998.1768
    • Beals, R., Sattinger, D. H. and Szmigielski, J. 1998 Acoustic scattering and the extended Korteweg-de Vries hierarchy. Adv. Math. 140, 190-206. (doi:10.1006/aima.1998.1768.)
    • (1998) Adv. Math , vol.140 , pp. 190-206
    • Beals, R.1    Sattinger, D.H.2    Szmigielski, J.3
  • 4
    • 18044392342 scopus 로고    scopus 로고
    • Multi-peakons and a theorem of Stieltjes
    • doi:10.1088/0266- 5611/15/1/001
    • Beals, R., Sattinger, D. H. and Szmigielski, J. 1999 Multi-peakons and a theorem of Stieltjes. Inv. Prob. 15, L1-L4. (doi:10.1088/0266- 5611/15/1/001.)
    • (1999) Inv. Prob , vol.15
    • Beals, R.1    Sattinger, D.H.2    Szmigielski, J.3
  • 5
    • 0001865962 scopus 로고
    • Model equations for long waves in nonlinear dispersive systems
    • Benjamin, T. B., Bona, J. L. and Mahony, J. J. 1972 Model equations for long waves in nonlinear dispersive systems. Phil. Trans. R. Soc. A 227, 47-78.
    • (1972) Phil. Trans. R. Soc. A , vol.227 , pp. 47-78
    • Benjamin, T.B.1    Bona, J.L.2    Mahony, J.J.3
  • 6
    • 12044254491 scopus 로고
    • An integrable shallow water equation with peaked solitons
    • doi:10.1103/PhysRevLett.71.1661
    • Camassa, R. and Holm, D. D. 1993 An integrable shallow water equation with peaked solitons. Phys. Rev. Lett. 71, 1661-1664. (doi:10.1103/PhysRevLett.71.1661.)
    • (1993) Phys. Rev. Lett , vol.71 , pp. 1661-1664
    • Camassa, R.1    Holm, D.D.2
  • 7
    • 0035848375 scopus 로고    scopus 로고
    • On the initial value problem for a completely integrable shallow water wave equation
    • doi:10.1016/S0375-9601 (01) 00070-6
    • Camassa, R. and Zenchuk, A. I. 2001 On the initial value problem for a completely integrable shallow water wave equation. Phys. Lett. A 281, 26-33. (doi:10.1016/S0375-9601 (01) 00070-6.)
    • (2001) Phys. Lett. A , vol.281 , pp. 26-33
    • Camassa, R.1    Zenchuk, A.I.2
  • 8
    • 56349110516 scopus 로고
    • A new integrable shallow water equation
    • Camassa, R., Holm, D. D. and Hyman, J. M. 1994 A new integrable shallow water equation. Adv. Appl. Mech. 31, 1-33.
    • (1994) Adv. Appl. Mech , vol.31 , pp. 1-33
    • Camassa, R.1    Holm, D.D.2    Hyman, J.M.3
  • 9
    • 34447130573 scopus 로고    scopus 로고
    • On the scattering problem for the Camassa-Holm equation
    • doi:10.1098/rspa.2000. 0701
    • Constantin, A. 2001 On the scattering problem for the Camassa-Holm equation. Proc. R. Soc. A 457, 953-970. (doi:10.1098/rspa.2000. 0701.)
    • (2001) Proc. R. Soc. A , vol.457 , pp. 953-970
    • Constantin, A.1
  • 10
    • 0031679566 scopus 로고    scopus 로고
    • Model equations for nonlinear dispersive waves in a compressible Mooney-Rivlin rod
    • doi:10.1007/BF01170373
    • Dai, H.-H. 1998a Model equations for nonlinear dispersive waves in a compressible Mooney-Rivlin rod. Acta Mech. 127, 193-207. (doi:10.1007/BF01170373.)
    • (1998) Acta Mech , vol.127 , pp. 193-207
    • Dai, H.-H.1
  • 11
    • 0040599108 scopus 로고    scopus 로고
    • Exact travelling-wave solutions of an integrable equation arising in hyperelastic rods
    • doi:10.1016/S0165-2125 (98) 00014-6
    • Dai, H.-H. 1998b Exact travelling-wave solutions of an integrable equation arising in hyperelastic rods. Wave Motion 28, 367-381. (doi:10.1016/S0165-2125 (98) 00014-6.)
    • (1998) Wave Motion , vol.28 , pp. 367-381
    • Dai, H.-H.1
  • 12
    • 0034347359 scopus 로고    scopus 로고
    • An inverse scattering scheme for the regularised long-wave equation
    • doi:10.1063/1.533278
    • Dye, J. M. and Parker, A. 2000 An inverse scattering scheme for the regularised long-wave equation. J. Math. Phys. 41, 2889-2904. (doi:10.1063/1.533278.)
    • (2000) J. Math. Phys , vol.41 , pp. 2889-2904
    • Dye, J.M.1    Parker, A.2
  • 13
    • 0001500560 scopus 로고    scopus 로고
    • The Camassa-Holm equation: Conserved quantities and the initial value problem
    • doi:10.1016/S0375-9601 (99) 00466-1
    • Fisher, M. and Schiff, J. 1999 The Camassa-Holm equation: conserved quantities and the initial value problem. Phys. Lett. A 259, 371-376. (doi:10.1016/S0375-9601 (99) 00466-1.)
    • (1999) Phys. Lett. A , vol.259 , pp. 371-376
    • Fisher, M.1    Schiff, J.2
  • 14
    • 0001702502 scopus 로고
    • On a class of physically important integrable equations
    • Fokas, A. S. 1995 On a class of physically important integrable equations. Physica D 87, 145-150.
    • (1995) Physica D , vol.87 , pp. 145-150
    • Fokas, A.S.1
  • 15
    • 22244482803 scopus 로고    scopus 로고
    • Some tricks from the symmetry-toolbox for nonlinear equations: Generalisations of the Camassa-Holm equation
    • Fuchssteiner, B. 1996 Some tricks from the symmetry-toolbox for nonlinear equations: generalisations of the Camassa-Holm equation. Physica D 95, 229-243.
    • (1996) Physica D , vol.95 , pp. 229-243
    • Fuchssteiner, B.1
  • 16
    • 49049150360 scopus 로고
    • Symplectic structures, their Bäcklund transformations and hereditary symmetries
    • Fuchssteiner, B. and Fokas, A. S. 1981 Symplectic structures, their Bäcklund transformations and hereditary symmetries. Physica D 4, 47-66.
    • (1981) Physica D , vol.4 , pp. 47-66
    • Fuchssteiner, B.1    Fokas, A.S.2
  • 17
    • 0002464716 scopus 로고
    • Direct methods in soliton theory
    • ed. R. K. Bullough and P. J. Caudrey, pp, Berlin: Springer
    • Hirota, R. 1980 Direct methods in soliton theory. In Solitons (ed. R. K. Bullough and P. J. Caudrey), pp. 157-176. Berlin: Springer.
    • (1980) Solitons , pp. 157-176
    • Hirota, R.1
  • 18
    • 1342300742 scopus 로고    scopus 로고
    • On solutions of the Camassa-Holm equation
    • doi:10.1098/rspa.2002.1078
    • Johnson, R. S. 2003 On solutions of the Camassa-Holm equation. Proc. R. Soc. A 459, 1687-1708. (doi:10.1098/rspa.2002.1078.)
    • (2003) Proc. R. Soc. A , vol.459 , pp. 1687-1708
    • Johnson, R.S.1
  • 19
    • 0001262723 scopus 로고
    • Reciprocal Bäcklund transformations of conservation laws
    • doi:10.1016/0375-9601 (82) 90081-0
    • Kingston, J. G. and Rogers, C. 1982 Reciprocal Bäcklund transformations of conservation laws. Phys. Lett. A 92, 261-264. (doi:10.1016/0375-9601 (82) 90081-0.)
    • (1982) Phys. Lett. A , vol.92 , pp. 261-264
    • Kingston, J.G.1    Rogers, C.2
  • 20
    • 0031535504 scopus 로고    scopus 로고
    • Convergence of solitary wave solutions in a perturbed bi-Hamiltonian dynamical system. I. Compactons and peakons
    • Li, Y. A. and Olver, P. J. 1997 Convergence of solitary wave solutions in a perturbed bi-Hamiltonian dynamical system. I. Compactons and peakons. Discrete Cont. Dyn. Sys. 3, 419-432.
    • (1997) Discrete Cont. Dyn. Sys , vol.3 , pp. 419-432
    • Li, Y.A.1    Olver, P.J.2
  • 21
    • 17144394784 scopus 로고    scopus 로고
    • The multiple-soliton solution of the Camassa-Holm equation
    • doi:10.1098/rspa.2004.1331
    • Li, Y. and Zhang, J. E. 2004 The multiple-soliton solution of the Camassa-Holm equation. Proc. R. Soc. A 460, 2617-2627. (doi:10.1098/rspa.2004.1331.)
    • (2004) Proc. R. Soc. A , vol.460 , pp. 2617-2627
    • Li, Y.1    Zhang, J.E.2
  • 23
    • 21844494238 scopus 로고
    • On exact solutions of the regularised long-wave equation: A direct approach to partially integrable equations I. Solitary wave and solitons
    • doi:10.1063/1.530976
    • Parker, A. 1995 On exact solutions of the regularised long-wave equation: a direct approach to partially integrable equations I. Solitary wave and solitons. J. Math. Phys. 36, 3498-3505. (doi:10.1063/1.530976.)
    • (1995) J. Math. Phys , vol.36 , pp. 3498-3505
    • Parker, A.1
  • 24
    • 0346684395 scopus 로고    scopus 로고
    • On soliton solutions of the Kaup-Kupershmidt equation. II. 'Anomalous' N-soliton solutions
    • Parker, A. 2000 On soliton solutions of the Kaup-Kupershmidt equation. II. 'Anomalous' N-soliton solutions. Physica D 137, 34-48.
    • (2000) Physica D , vol.137 , pp. 34-48
    • Parker, A.1
  • 25
    • 17144414968 scopus 로고    scopus 로고
    • On the Camassa-Holm equation and a direct method of solution. I. Bilinear form and solitary waves
    • doi:10.1098/rspa.2004.1301
    • Parker, A. 2004 On the Camassa-Holm equation and a direct method of solution. I. Bilinear form and solitary waves. Proc. R. Soc. A 460, 2929-2957. (doi:10.1098/rspa.2004.1301.)
    • (2004) Proc. R. Soc. A , vol.460 , pp. 2929-2957
    • Parker, A.1
  • 26
    • 0002632382 scopus 로고    scopus 로고
    • The Camassa-Holm equation: A loopgroup approach
    • Schiff, J. 1998 The Camassa-Holm equation: a loopgroup approach. Physica D 121, 24-43.
    • (1998) Physica D , vol.121 , pp. 24-43
    • Schiff, J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.