Abstract
Let us first compare some results concerning invariance properties in the Painlevé analysis of a partial differential equation
which depends polynomially on its solution u and its partial derivatives Du with respect to x and t. Considering a series expansion for u in the neighbourhood of the singular manifold ϕ(x,t) = 0, we are looking for, as a solution of (1), the formal expression
where the expansion variable x goes to zero as ϕ in the following way:
and the coefficients α, β, γ and uj are only functions of the derivatives Dϕ of ϕ.
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References
Weiss J., Tabor M. and Carnevale G., J. Math. Phys. 24, 522 (1983).
Conte R., P.L.A. 140, 383 (1989).
Conte R. and Musette M., J. Phys. A: Math. Gen. 22, 169 (1989).
Levi D., Rep. on Math. Phys. 23, 41 (1986) Levi D. and Ragnisco A., Inverse Problems 4, 815 (1989).
Musette M., “Painlevé analysis for integrable and nonintegrable p.d.e.’s” presented at the VI International Workshop “Solitons and applications”, 25-27 august 1989, Dubna, USSR - VUB/TENA/89/10.
Wahlquist H.D. and Estabrook F.B., J. Math. Phys. J.6, 1 (1975) Estabrook F.B. and Wahlquist H.D., J. Math. Phys. 17, 1293 (1976).
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© 1990 Springer-Verlag Berlin Heidelberg
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Musette, M. (1990). Painlevé-Darboux Transformation in Nonlinear PDEs. In: Sabatier, P.C. (eds) Inverse Methods in Action. Inverse Problems and Theoretical Imaging. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-75298-8_71
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DOI: https://doi.org/10.1007/978-3-642-75298-8_71
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