Travelling wave solutions for a second order wave equation of KdV type

Applied Mathematics and Mechanics (English Edition)

Volumn 28, Issue 11, 2007, Pages 1455-1465

  Long, Yao ^a   Li, Ji Bin ^b,c   Rui, Wei Guo ^a   He, Bin ^a  

^a HONGHE UNIVERSITY   (China)

^b ZHEJIANG NORMAL UNIVERSITY   (China)

^c KUNMING UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

Author keywords

Kink wave and anti kink wave solutions; Periodic wave solution; Smooth and non smooth periodic waves; Solitary wave solution

Indexed keywords

NONLINEAR EQUATIONS; PARAMETER ESTIMATION; SOLITONS; TRAVELING WAVE ANTENNAS; WAVE EQUATIONS;

KINK WAVES; NON-SMOOTH PERIODIC WAVES; PERIODIC WAVE SOLUTIONS; SOLITARY WAVE SOLUTIONS;

DYNAMICAL SYSTEMS;

EID: 38049119872     PISSN: 02534827     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10483-007-1105-y     Document Type: Article

References (12)

1. Tzirtzilakis E, Xenos M, Marinakis V, Bountis T. Interactions and stability of solitary waves in shallow water[J]. Chaos, Solitons and Fractals, 2002, 14(1):87-95.
2. Tzirtzilakis E, Marinakis V, Apokis C, Bountis T. Soliton-like solutions of higher order wave equations of the Korteweg-de-Vries Type[J]. J Math Phys, 2002, 43(12):6151-6161.
3. Fokas A S. On a class of physically important integral equations[J]. Physica D, 1995, 87(1-4):145-150.
4. Long Yao, Rui Weiguo, He Bin. Travelling wave solutions for a higher order wave equations of KdV type (I)[J]. Chaos, Solitons and Fractals, 2005, 23(2):469-475.
5. Li Jibin, Dai Huihui, On the studies of sigular travelling wave equations: dynamical system approach[M]. Beijing: Science Press, 2007 (in Chiese).
6. Chow S N, Hale J K. Method of bifurcation theory[M]. New York: Springer-Verlag, 1981.
7. Guckenheimer J, Holmes P J. Nonlinear oscillations, dynamical systems and bifurcations of vector fields[M]. New York: Springer-Verlag, 1983.
8. Perko L. Differential equations and dynamical systems[M]. New York: Springer-Verlag, 1991.
9. Li Y A, Olver P J. Convergence of solitary-wave solutions in a perturbed bi-Hamiltonian dynamical system I: compactons and peakons[J]. Discrete and Continuous Dynamical Systems, 1997, 3(3):419-432.
10. Li Y A, Olver P J. Convergence of solitary-wave solutions in a perturbed bi-Hamiltonian dynamical system II: complex analytic behaviour and convergence to non-analytic solutions[J]. Discrete and Continuous Dynamical Systems, 1998, 4(1):159-191.
11. Li Jibin, Liu Zhenrong. Smooth and non-smooth travelling waves in a nonlinearly dispersive equation[J]. Appl Math Modelling, 2000, 25(1):41-56.
12. Li Jibin, Liu Zhenrong, Travelling wave solutions for a class of nonlinear dispersive equations[J]. Chin Ann of Math, 2002, 23B(3):397-418.