Geodesic
Exact soliton solutions for the general fifth Korteweg–de Vries equation
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 8, pp. 1497-1502 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

With the aid of computer symbolic computation system such as Maple, the extended hyperbolic function method and the Hirota's bilinear formalism combined with the simplified Hereman form are applied to determine the soliton solutions for the general fifth-order KdV equation. Several new soliton solutions can be obtained if we taking parameters properly in these solutions. The employed methods are straightforward and concise, and they can also be applied to other nonlinear evolution equations in mathematical physics. 
@article{ZVMMF_2009_49_8_a11,
     author = {W. Long},
     title = {Exact soliton solutions for the general fifth {Korteweg{\textendash}de} {Vries} equation},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1497--1502},
     year = {2009},
     volume = {49},
     number = {8},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_8_a11/}
}
TY  - JOUR
AU  - W. Long
TI  - Exact soliton solutions for the general fifth Korteweg–de Vries equation
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2009
SP  - 1497
EP  - 1502
VL  - 49
IS  - 8
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_8_a11/
LA  - en
ID  - ZVMMF_2009_49_8_a11
ER  - 
%0 Journal Article
%A W. Long
%T Exact soliton solutions for the general fifth Korteweg–de Vries equation
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2009
%P 1497-1502
%V 49
%N 8
%U http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_8_a11/
%G en
%F ZVMMF_2009_49_8_a11
W. Long. Exact soliton solutions for the general fifth Korteweg–de Vries equation. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 8, pp. 1497-1502. http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_8_a11/

[1] K. Sawada, T. Kotera, “A method for finding $N$-soliton solutions for the KdV equation and KdV-like equation”, Prog. Theor. Phys., 51 (1974), 1355–1367 | DOI | MR | Zbl

[2] A. M. Wazwaz, “Abundant solitons solutions for several forms of the fifth-order KdV equation by using the tanh method”, Appl. Math. Comput., 182 (2006), 283–300 | DOI | MR | Zbl

[3] A. M. Wazwaz, “The extended tanh method for new solitons solutions for many forms of the fifth-order KdV equations”, Appl. Math. Comput., 184 (2007), 1002–1014 | DOI | MR | Zbl

[4] A. M. Wazwaz, “Analytic study on the generalized fifth-order KdV equation: New solitons and periodic solutions”, Commun. Nonlinear Sci. Numer. Simul., 12 (2007), 1172–1180 | DOI | MR | Zbl

[5] S. Gómes, “The extended tanh method for new solitons solutions for many forms of the fifth-order KdV equations”, Appl. Math. Comput., 189 (2007), 1066–1077 | DOI | MR

[6] A. Salas, Exact solutions for the general fifth KdV equation by the exp function method, In press

[7] P. D. Lax, “Integrals of nonlinear equations of evolution and solitary waves”, Commun. Pure Appl. Math., 62 (1968), 467–490 | DOI | MR

[8] D. Kaup, “On the inverse scattering problem for the cubic eigenvalue problems of the class $\Psi_{xxx}+6Q\Psi_x+6R\Psi=\lambda\Psi$”, Stud. Appl. Math., 62 (1980), 189–216 | MR | Zbl

[9] B. A. Kupershmidt, “A super KdV equation: an integrable system”, Phys. Lett. A, 102 (1984), 213–215 | DOI | MR

[10] M. Ito, “A reduce program for finding symmetries of nonlinear evolution equations with uniform rank”, Comp. Phys. Comm., 42 (1986), 351–357 | DOI | MR

[11] R. Hirota, The Direct Method in Soliton Theory, Cambridge University Press, Cambridge, 2004 | MR | Zbl

[12] M. Ablowitz, H. Segur, Solitons and the Inverse Scattering Transform, SIAM, Philadelphia, 1981 | MR | Zbl

[13] A. M. Wazwaz, “Multiple-soliton solutions for the fifth-order Caudrey–Dodd–Gibbon equation”, Appl. Math. Comput., 197 (2008), 719–724 | DOI | MR | Zbl

[14] A. M. Wazwaz, “The Hirota's direct method and the tanh-coth method for multiple-soliton solutions of the Sawada–Kotera–Ito seventh-order equation”, Appl. Math. Comput., 199 (2008), 133–138 | DOI | MR | Zbl

[15] A. M. Wazwaz, “TV-soliton solutions for the combined KdV-CDG equation and the KdV-Lax equation”, Appl. Math. Comput., 203 (2008), 402–407 | DOI | MR | Zbl

[16] A. M. Wazwaz, Single and multiple-soliton solutions for the (2+1)-dimensional KdV, In Press Appl. Math. Comput., 2008

[17] A. M. Wazwaz, “The extended tanh method for new solitons solutions for many forms of the fifth-order KdV equations”, Appl. Math. Comput., 184:2 (2007), 1002–1014 | DOI | MR | Zbl

[18] A. M. Wazwaz, “The tanh-conth method for solitons and kink solutions for nonlinear parabolic equations”, Appl. Math. Comput., 188 (2007), 1467–1475 | DOI | MR | Zbl

[19] A. M. Wazwaz, “New solitary-wave special solutions with compact support for the nonlinear dispersive $K(m,n)$ equations”, Chaos, Solitons and Fractals, 13:2 (2002), 321–330 | DOI | MR | Zbl