Abstract
We consider generalizations of the earlier results, obtained for one-dimensional equations of the Kadomtsev–Petviashvili (KP) class, to two- and three-dimensional KP-class equations with an arbitrary nonlinearity index with allowance for the higher-order dispersion correction and terms describing dissipation and instability. The asymptotics of soliton and nonsoliton solutions are derived. Constructing phase portraits in the 8-dimensional space based on the results of a qualitative analysis of generalized Korteweg–de Vries (KdV) equations is discussed.
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REFERENCES
V. Yu. Belashov and S. G. Tyunina, Izv. Vyssh. Uchebn. Zaved., Radiofiz., 40, No. 3, 328 (1997).
V. I. Karpman and V. Yu. Belashov, “Structure of two-dimensional oscillating solitons in weakly dispersive media” [in Russian], preprint No. 25(972), Institute of Terrestrial Magnetism, the Ionosphere, and Radio Wave Propagation, Russian Academy of Sciences, Moscow (1991).
V. Yu. Belashov, The KP Equation and its Generalizations: Theory and Applications [in Russian], North-East Complex Research Institute of the Far East Branch of the Russian Academy of Sciences, Magadan (1997).
B. B. Kadomtsev and V. I. Petviashvili, Dokl. Akad. Nauk SSSR, 192, No. 4, 753 (1970).
V. I. Petviashvili, Fiz. Plazmy, 2, No. 3, 496 (1976).
V. I. Karpman and V. Yu. Belashov, Phys. Lett. A, 154, Nos. 3-4, 131 (1991).
V. I. Karpman and V. Yu. Belashov, Phys. Lett. A, 154, Nos. 3-4, 140 (1991).
V. Yu. Belashov, Phys. Lett. A, 197, 282 (1995).
T. Kawahara, Phys. Rev. Lett., 51, No. 5, 381 (1983).
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Belashov, V.Y. Structure of the Solutions of Generalized Kadomtsev–Petviashvili Equations. Radiophysics and Quantum Electronics 45, 376–380 (2002). https://doi.org/10.1023/A:1019680127227
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DOI: https://doi.org/10.1023/A:1019680127227