메뉴 건너뛰기




Volumn 170, Issue 1, 2005, Pages 347-360

The Camassa-Holm-KP equations with compact and noncompact travelling wave solutions

Author keywords

Camassa Holm KP equation; Compactons; Periodic solutions; Sine Cosine method; Solitary patterns solutions; Solitons; The tanh method

Indexed keywords

NONLINEAR SYSTEMS;

EID: 26844449486     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2004.12.002     Document Type: Article
Times cited : (54)

References (34)
  • 1
    • 0035517241 scopus 로고    scopus 로고
    • Introduction to solitons
    • M. Wadati Introduction to solitons Pramana: J. Phys. 57 5-6 2001 841 847
    • (2001) Pramana: J. Phys. , vol.57 , Issue.5-6 , pp. 841-847
    • Wadati, M.1
  • 2
    • 0347821899 scopus 로고
    • The exact solution of the modified Kortweg-de Vries equation
    • M. Wadati The exact solution of the modified Kortweg-de Vries equation J. Phys. Soc. Jpn. 32 1972 1681 1687
    • (1972) J. Phys. Soc. Jpn. , vol.32 , pp. 1681-1687
    • Wadati, M.1
  • 3
    • 0007690397 scopus 로고
    • The modified Kortweg-de Vries equation
    • M. Wadati The modified Kortweg-de Vries equation J. Phys. Soc. Jpn. 34 1973 1289 1296
    • (1973) J. Phys. Soc. Jpn. , vol.34 , pp. 1289-1296
    • Wadati, M.1
  • 5
    • 0037298204 scopus 로고    scopus 로고
    • Cylindrical solitary pulses in a two-dimensional stabilized Kuramoto-Sivashinsky system
    • B. Feng, B. Malomed, and T. Kawahara Cylindrical solitary pulses in a two-dimensional stabilized Kuramoto-Sivashinsky system Physica D 2003 127 138
    • (2003) Physica D , pp. 127-138
    • Feng, B.1    Malomed, B.2    Kawahara, T.3
  • 6
    • 84976168869 scopus 로고
    • A modified Korteweg-de-Vries equation for ion acoustic waves due to resonant electrons
    • H. Schamel A modified Korteweg-de-Vries equation for ion acoustic waves due to resonant electrons J. Plasma Phys. 9 3 1973 377 387
    • (1973) J. Plasma Phys. , vol.9 , Issue.3 , pp. 377-387
    • Schamel, H.1
  • 7
    • 0041736716 scopus 로고    scopus 로고
    • Exact travelling wave solutions for a generalized Zakharov-Kuznetsov equation
    • B. Li, Y. Chen, and H. Zhang Exact travelling wave solutions for a generalized Zakharov-Kuznetsov equation Appl. Math. Comput. 146 2003 653 666
    • (2003) Appl. Math. Comput. , vol.146 , pp. 653-666
    • Li, B.1    Chen, Y.2    Zhang, H.3
  • 8
    • 0001384053 scopus 로고    scopus 로고
    • Self-focusing and transverse instabilities of solitary waves
    • Y.S. Kivshar, and D.E. Pelinovsky Self-focusing and transverse instabilities of solitary waves Phys. Rep. 331 2000 117 195
    • (2000) Phys. Rep. , vol.331 , pp. 117-195
    • Kivshar, Y.S.1    Pelinovsky, D.E.2
  • 9
    • 10044298719 scopus 로고
    • The stability of solitary waves in weakly dispersive media
    • B.B. Kadomtsev, and V.I. Petviashvili The stability of solitary waves in weakly dispersive media Sov. Phys. JETP 39 1974 285 295
    • (1974) Sov. Phys. JETP , vol.39 , pp. 285-295
    • Kadomtsev, B.B.1    Petviashvili, V.I.2
  • 10
    • 0001762098 scopus 로고
    • On three-dimensional solitons
    • V.E. Zakharov, and E.A. Kuznetsov On three-dimensional solitons Sov. Phys. 39 1974 285 288
    • (1974) Sov. Phys. , vol.39 , pp. 285-288
    • Zakharov, V.E.1    Kuznetsov, E.A.2
  • 11
    • 0001078296 scopus 로고    scopus 로고
    • The derivation of a modified Zakharov-Kuznetsov equation and the stability of its solutions
    • S. Monro, and E.J. Parkes The derivation of a modified Zakharov-Kuznetsov equation and the stability of its solutions J. Plasma Phys. 62 3 1999 305 317
    • (1999) J. Plasma Phys. , vol.62 , Issue.3 , pp. 305-317
    • Monro, S.1    Parkes, E.J.2
  • 12
    • 0034289227 scopus 로고    scopus 로고
    • Stability of solitary-wave solutions to a modified Zakharov-Kuznetsov equation
    • S. Monro, and E.J. Parkes Stability of solitary-wave solutions to a modified Zakharov-Kuznetsov equation J. Plasma Phys. 64 3 2000 411 426
    • (2000) J. Plasma Phys. , vol.64 , Issue.3 , pp. 411-426
    • Monro, S.1    Parkes, E.J.2
  • 13
    • 12044253199 scopus 로고
    • Compactons: Solitons with finite wavelengths
    • P. Rosenau, and J.M. Hyman Compactons: solitons with finite wavelengths Phys. Rev. Lett. 70 5 1993 564 567
    • (1993) Phys. Rev. Lett. , vol.70 , Issue.5 , pp. 564-567
    • Rosenau, P.1    Hyman, J.M.2
  • 14
    • 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 11 1993 1661 1664
    • (1993) Phys. Rev. Lett. , vol.71 , Issue.11 , pp. 1661-1664
    • Camassa, R.1    Holm, D.2
  • 15
    • 0000814560 scopus 로고    scopus 로고
    • Peakons and cashoidal waves: Travelling wave solutions of the Camassa-Holm equation
    • J.P. Boyd Peakons and cashoidal waves: travelling wave solutions of the Camassa-Holm equation Appl. Math. Comput. 81 2-3 1997 173 187
    • (1997) Appl. Math. Comput. , vol.81 , Issue.2-3 , pp. 173-187
    • Boyd, J.P.1
  • 16
    • 0041760859 scopus 로고    scopus 로고
    • Characteristics and the initial value problem of a completely integrable shallow water equation
    • R. Camassa Characteristics and the initial value problem of a completely integrable shallow water equation Discr. Continuous Dynam. Syst. - Series B 3 1 2003 115 139
    • (2003) Discr. Continuous Dynam. Syst. - Series B , vol.3 , Issue.1 , pp. 115-139
    • Camassa, R.1
  • 17
    • 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 51 79
    • (2002) J. Phys. A , vol.35 , pp. 51-79
    • Constantin, A.1    Kolev, B.2
  • 18
    • 0004483962 scopus 로고    scopus 로고
    • The tanh method. I. Exact solutions of nonlinear evolution and wave equations
    • W. Malfliet The tanh method. I. Exact solutions of nonlinear evolution and wave equations Phys. Scr. 54 1996 563 568
    • (1996) Phys. Scr. , vol.54 , pp. 563-568
    • Malfliet, W.1
  • 19
    • 0000068096 scopus 로고    scopus 로고
    • The tanh method. II. Perturbation technique for conservative systems
    • W. Malfliet The tanh method. II. Perturbation technique for conservative systems Phys. Scr. 54 1996 569 575
    • (1996) Phys. Scr. , vol.54 , pp. 569-575
    • Malfliet, W.1
  • 20
    • 0038111998 scopus 로고    scopus 로고
    • Peaked wave solutions of Camassa-Holm equation
    • Z. Liu, R. Wang, and Z. Jing Peaked wave solutions of Camassa-Holm equation Chaos Solitons Fractals 19 2004 77 92
    • (2004) Chaos Solitons Fractals , vol.19 , pp. 77-92
    • Liu, Z.1    Wang, R.2    Jing, Z.3
  • 21
    • 0036502719 scopus 로고    scopus 로고
    • Peakons of the Camassa-Holm equation
    • Z. Liu, and T. Qian Peakons of the Camassa-Holm equation Appl. Math. Modell. 26 2002 473 480
    • (2002) Appl. Math. Modell. , vol.26 , pp. 473-480
    • Liu, Z.1    Qian, T.2
  • 22
    • 0034825095 scopus 로고    scopus 로고
    • Peakons and periodic cusp waves in a generalized Camassa-Holm equation
    • T. Qian, and M. Tang Peakons and periodic cusp waves in a generalized Camassa-Holm equation Chaos Solitons Fractals 12 2001 1347 1360
    • (2001) Chaos Solitons Fractals , vol.12 , pp. 1347-1360
    • Qian, T.1    Tang, M.2
  • 23
    • 0043132083 scopus 로고    scopus 로고
    • New peaked solitary wave solutions of the generalized Camassa-Holm equation
    • L. Tian, and X. Song New peaked solitary wave solutions of the generalized Camassa-Holm equation Chaos Solitons Fractals 19 2004 621 637
    • (2004) Chaos Solitons Fractals , vol.19 , pp. 621-637
    • Tian, L.1    Song, X.2
  • 24
    • 14544289465 scopus 로고    scopus 로고
    • New compact and noncompact solutions for variants of a modified Camassa-Holm equation
    • in press
    • A.M. Wazwaz, New compact and noncompact solutions for variants of a modified Camassa-Holm equation, Appl. Math. Comput., in press.
    • Appl. Math. Comput.
    • Wazwaz, A.M.1
  • 25
    • 17644367140 scopus 로고    scopus 로고
    • A class of nonlinear fourth order variant of a generalized Camassa-Holm equation with compact and noncompat solutions
    • in press
    • A.M. Wazwaz, A class of nonlinear fourth order variant of a generalized Camassa-Holm equation with compact and noncompat solutions, Appl. Math. Comput., in press.
    • Appl. Math. Comput.
    • Wazwaz, A.M.1
  • 27
    • 0036462771 scopus 로고    scopus 로고
    • New solitary-wave special solutions with compact support for the nonlinear dispersive K(m, n) equations
    • A.M. Wazwaz New solitary-wave special solutions with compact support for the nonlinear dispersive K(m, n) equations Chaos Solitons Fractals 13 2 2002 321 330
    • (2002) Chaos Solitons Fractals , vol.13 , Issue.2 , pp. 321-330
    • Wazwaz, A.M.1
  • 28
    • 0036028182 scopus 로고    scopus 로고
    • Exact specific solutions with solitary patterns for the nonlinear dispersive K(m, n) equations
    • A.M. Wazwaz Exact specific solutions with solitary patterns for the nonlinear dispersive K(m, n) equations Chaos Solitons Fractals 13 1 2001 161 170
    • (2001) Chaos Solitons Fractals , vol.13 , Issue.1 , pp. 161-170
    • Wazwaz, A.M.1
  • 29
    • 0037114102 scopus 로고    scopus 로고
    • General compactons solutions for the focusing branch of the nonlinear dispersive K(n, n) equations in higher dimensional spaces
    • A.M. Wazwaz General compactons solutions for the focusing branch of the nonlinear dispersive K(n, n) equations in higher dimensional spaces Appl. Math. Comput. 133 2/3 2002 213 227
    • (2002) Appl. Math. Comput. , vol.133 , Issue.23 , pp. 213-227
    • Wazwaz, A.M.1
  • 30
    • 0037114104 scopus 로고    scopus 로고
    • General solutions with solitary patterns for the defocusing branch of the nonlinear dispersive K(n, n) equations in higher dimensional spaces
    • A.M. Wazwaz General solutions with solitary patterns for the defocusing branch of the nonlinear dispersive K(n, n) equations in higher dimensional spaces Appl. Math. Comput. 133 2/3 2002 229 244
    • (2002) Appl. Math. Comput. , vol.133 , Issue.23 , pp. 229-244
    • Wazwaz, A.M.1
  • 31
    • 0037451839 scopus 로고    scopus 로고
    • An analytic study of compactons structures in a class of nonlinear dispersive equations
    • A.M. Wazwaz An analytic study of compactons structures in a class of nonlinear dispersive equations Math. Comput. Simul. 63 1 2003 35 44
    • (2003) Math. Comput. Simul. , vol.63 , Issue.1 , pp. 35-44
    • Wazwaz, A.M.1
  • 32
    • 0037429584 scopus 로고    scopus 로고
    • A study on nonlinear dispersive partial differential equations of compact and noncompact solutions
    • A.M. Wazwaz A study on nonlinear dispersive partial differential equations of compact and noncompact solutions Appl. Math. Comput. 135 2-3 2003 399 409
    • (2003) Appl. Math. Comput. , vol.135 , Issue.2-3 , pp. 399-409
    • Wazwaz, A.M.1
  • 33
    • 0037429574 scopus 로고    scopus 로고
    • A construction of compact and noncompact solutions of nonlinear dispersive equations of even order
    • A.M. Wazwaz A construction of compact and noncompact solutions of nonlinear dispersive equations of even order Appl. Math. Comput. 135 2-3 2003 324 411
    • (2003) Appl. Math. Comput. , vol.135 , Issue.2-3 , pp. 324-411
    • Wazwaz, A.M.1
  • 34
    • 0037370153 scopus 로고    scopus 로고
    • Compactons in a class of nonlinear dispersive equations
    • A.M. Wazwaz Compactons in a class of nonlinear dispersive equations Math. Comput. Modell. 37 3/4 2003 333 341
    • (2003) Math. Comput. Modell. , vol.37 , Issue.34 , pp. 333-341
    • Wazwaz, A.M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.