Numerical Estimation of Traveling Wave Solution of Two-Dimensional K-dV Equation Using a New Auxiliary Equation Method

Show more

References

[1] Yu. N. Zaiko, “Quasiperiodic Solutions of the Kortewegd Vries Equation,” Technical Physics Letters, Vol. 28. No. 3, 2002, pp. 235-236. doi:10.1134/1.1467286

[2] F. L. Qu and W. Q. Wang, “Alternating Segment Explicit—Implicit Scheme for Nonlinear Third-Order KdV Equation,” Applied Mathematics and Mechanics, Vol. 28, No. 7, 2007, pp. 973-980. doi:10.1007/s10483-007-0714-y

[3] N. E. Zhukovskii, “Hydraulic Shock in water Pipelines,” Gostekhteorizdal, Moscow, 1949.

[4] A. C. Newell, “Solitons in Mathematics and Physics,” SIAM, Philadelphia, 1985.

[5] V. A. Rukavishnikov and O. P. Tkachenko, “The Korteweg-de Vries Equation in a Cylindrical Pipe,” Computational Mathematics and Mathematical Physics, Vol. 48, No. 1, 2008, pp. 139-146.
doi:10.1134/S0965542508010107

[6] N. Smaoui and R. H. Al-Jamal, “Boundary Control of the Generalized Korteweg-de Vries-Burgers Equation,” Nonlinear Dynamics, Vol. 51, 2008, pp. 439-446.

[7] J. Pang, C.-Q. Bian and L. Chao, “A New Auxiliary Equation Method for Finding Traveling Wave Solution to K-dV Equation,” Applied Mathematics and Mechanics (English Edition), Vol. 31, No. 7, 2010, pp. 929-936.

[8] L. Debnath, “Linear Partial Differential Equations for Scientists and Engineers,” 4th Edition, Tyn Myint-U, 2007, pp. 573-580.

[9] R. L. Herman, “Solitary Waves,” American Scientist, Vol. 80, 1992, pp. 350-361.

[10] P. A. Clarkson and M. D. Kruskal, “New Similarity Reductions of the Boussinesq Equation,” Journal of Mathematical Physics, Vol. 30, No. 10, 1989, pp. 2201-2213.
doi:10.1063/1.528613