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Freedom in the expansion and obstacles to integrability in multiple-soliton solutions of the perturbed KdV equation. (English) Zbl 1099.35124
From the summary: The construction of solutions of the perturbed KdV equation encounters obstacles to asymptotic integrability beyond the first order, when the zero-order approximation is not a single-soliton wave. In the standard analysis, the obstacles lead to the loss of integrability of the normal form, resulting in a zero-order term, which does not have the simple structure of the solution of the unperturbed equation. Exploiting the freedom in the perturbative expansion, an algorithm is proposed that shifts the effect of the obstacles from the normal form to the higher-order terms.

35Q53KdV-like (Korteweg-de Vries) equations
37K40Soliton theory, asymptotic behavior of solutions
37K55Perturbations, KAM for infinite-dimensional systems
Full Text: DOI
[1] Korteweg, D. J.; De Vries, G.: Phil. mag.. 39, 422 (1895)
[2] Kodama, Y.: Phys. lett. A. 112, 193 (1985)
[3] Kodama, Y.: Physica D. 16, 14 (1985)
[4] Kodama, Y.: Normal form and solitons. Topics in soliton theory and exactly solvable nonlinear equation, 319-340 (1987) · Zbl 0736.35099
[5] Kodama, Y.; Mikhailov, A. V.: Obstacles to asymptotic integrability. Algebraic aspects of integrable systems, 173-204 (1997) · Zbl 0867.35091
[6] Kraenkel, R. A.; Manna, M. A.; Merle, V.; Montero, J. C.; Pereira, J. G.: Phys. rev. E. 54, 2976 (1996)
[7] Kraenkel, R. A.: Phys. rev. E. 57, 4775 (1998)
[8] Hiraoka, Y.; Kodama, Y.: Normal form and solitons. Lecture notes, euro summer school, 2001 (2002)
[9] Zakharov, V. E.; Manakov, S. V.: Sov. phys. JETP. 44, 106 (1976)
[10] Kodama, Y.; Taniuti, T.: J. phys. Soc. Japan. 45, 298 (1978)
[11] Kraenkel, R. A.; Manna, M. A.; Pereira, J. G.: J. math. Phys.. 36, 307 (1995)
[12] Hirota, R.: Exact solution of the Korteweg--de Vries equation for multiple interactions of solitons. Phys. rev. Lett. 27, 1192-1194 (1971) · Zbl 1168.35423
[13] Gardner, C. S.; Greene, J. M.; Kruskal, M. D.; Miura, R. M.: Phys. rev. Lett.. 19, 1095 (1967)
[14] Miura, R. M.: J. math. Phys.. 9, 1202 (1968)
[15] Miura, R. M.; Gardner, C. S.; Kruskal, M. D.: J. math. Phys.. 9, 1204 (1968)
[16] Su, C. H.; Gardner, C. S.: J. math. Phys.. 10, 536 (1969)
[17] Kruskal, M. D.; Miura, R. M.; Gardner, C. S.: J. math. Phys.. 11, 952 (1970)
[18] Gardner, C. S.: J. math. Phys.. 12, 1548 (1971) · Zbl 0238.00002
[19] Gardner, C. S.; Greene, J. M.; Kruskal, M. D.; Miura, R. M.: Comm. pure appl. Math.. 27, 97 (1974)
[20] Lax, P. D.: Comm. pure appl. Math.. 21, 467 (1968)
[21] Lax, P. D.: Comm. pure appl. Math.. 28, 141 (1975)
[22] Ablowitz, M. J.; Segur, H.: Solitons and the inverse scattering transforms. (1981) · Zbl 0472.35002
[23] Newell, A. C.: Solitons in mathematics and physics. (1985) · Zbl 0565.35003
[24] Ablowitz, M. J.; Clarkson, P. A.: Solitons, nonlinear evolution equations and inverse scattering. (1991) · Zbl 0762.35001
[25] Kahn, P. B.; Zarmi, Y.: Nonlinear dynamics: exploration through normal forms. (1998) · Zbl 1053.37067
[26] Li, Y.; Sattinger, D. H.: J. math. Fluid mech.. 1, 117 (1999)