You are here

Two types of traveling wave solutions of a KdV-like advection-dispersion equation

Journal Name:

Publication Year:

Abstract (2. Language): 
We present a KdV-like 2-parameter equation ut + (3(1 − δ)u + (δ + 1)uxx ux )ux = ϵuxxx. By using the dynamical system method, existence of different traveling wave solutions are discussed, including smooth solitary wave solution of with bell type, solitary wave solutions of valley type and peakon wave solution of valley type. Numerical integration are used to shown the different types of solutions.
273-282

REFERENCES

References: 

[1] J. Lenells, Traveling wave solutions of the Camassa-Holm equation and
Korteweg-de Vries equations, J. Nonlinear Math. Phys. 11 (2004) 508–
520.
[2] R. Camsssa, D. D. Holm, J. M. Hyman, An integrable shallow water
equation with peaked solitons, Phys. Rev. Lett. 71 (1993) 1661–1664.
[3] A. Biswas, Solitary wave solution for the generalized KdV equation with
time-dependent damping and dispersion, Commun. Nonlinear Sci. Numer.
Simul. 14 (9-10) (2009) 3503–3506.
[4] L. Wazzan, A modified tanh-coth method for solving the KdV and the
KdV-Burgers’ equations, Commun. Nonlinear Sci. Numer. Simul. 14 (2)
(2009) 443–450.
[5] H. Bin, L. Jibin, L. Yao, R. Weiguo, Bifurcations of travelling wave solutions
for a variant of camassa-holm equation, Nonlinear Analysis: Real
World Applications 9 (2) (2008) 222 – 232.
[6] A.-M. Wazwaz, Peakons, kinks, compactons and solitary patterns solutions
for a family of Camassa-Holm equations by using new hyperbolic
schemes, Appl. Math. Comput. 182 (1) (2006) 412–424.
[7] J. Li, Exact explicit peakon and periodic cusp wave solutions for several
nonlinear wave equations, J. Dynam. Differential Equations 20 (4) (2008)
909–922.
[8] A. Sen, D. P. Ahalpara, A. Thyagaraja, G. S. Krishnaswami, A kdvlike
advection-dispersion equation with some remarkable properties, arXiv:
1109.3745v1 [nlin.PS].[9] Z. Qiao, J. Li, Negative-order kdv equation with both solitons
and kink wave solutions, EPL 94 (3) (2001) 50003,doi:10.1209/0295–
5075/94/50003.
[10] J. B. Li, H. H. Dai, On the Study of Singular Nonlinear Travelling Wave
Equations: Dynamical Approach, Science Press, Beijing, 2007.

Thank you for copying data from http://www.arastirmax.com