Abstract
For nonlinear partial differential equations that cannot be integrated by the inverse scattering method, an approach that makes it possible to construct Wahlquist—Estabrook approximating pseudopotentials is proposed. The method is used to find an approximate Lax pair and conservation laws of the Kawahara equation.
Similar content being viewed by others
References
H. D. Wahlquist and F. B. Estabrook,J. Math. Phys.,16, 1 (1975).
D. J. Kaup,Physica (Utrecht) D 1, 391 (1980).
J. Corones,J. Math. Phys.,17, 756 (1976).
M. C. Nucci,J. Phys. A,22, 2897 (1989).
L. A. Takhtadzhan and L. D. Faddeev,The Hamiltonian Approach in the Theory of Solitons [in Russian], Nauka, Moscow (1986).
D. J. Kaup,SIAM J. Appl. Math. 31, 121 (1976).
V. I. Karpman and V. I. Maslov,Zh. Eksp. Teor. Phys.,73, 537 (1977).
V. I. Karpman,Zh. Eksp. Teor. Fiz.,77, 114 (1979).
K. Yoshimura and S. Watanabe,J. Phys. Soc. (Jpn.),51, 3025 (1982).
A. T. Il'ichev and A. V. Marchenko,Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 1, 88 (1989).
C. S. Gardner, J. M. Greene, M. D. Kruskul, and R. M. Miura,Phys. Rev. Lett.,19, 1095 (1967).
M. J. Ablowitz and H. Segur,Solitons and the Inverse Scattering Transform (SIAM Studies in Applied Maths., Vol 4), Philadelphia (1981).
A. T. Il'ichev,Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 2, 99 (1990).
Additional information
Moscow Engineering Physics Institute. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 91, No. 3, pp. 355–362, June, 1992.
Rights and permissions
About this article
Cite this article
Alekseev, A.A., Kudryashov, N.A. Approximating pseudopotentials for evolution equations containing a small parameter. Theor Math Phys 91, 575–580 (1992). https://doi.org/10.1007/BF01017332
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01017332