Symmetry of the KP-type solitary waves

Esfahani, Amin; Levandosky, Steve

doi:10.1090/proc/14617

Symmetry of the KP-type solitary waves
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by Amin Esfahani and Steve Levandosky PDF

Proc. Amer. Math. Soc. 147 (2019), 3867-3875 Request permission

Abstract:

In this paper, we study the behavior of the solitary waves of the rotation-modified Kadomtsev-Petviashvili equation. By knowing the symmetry of solitary waves in the transverse direction, we improve the previous results and show that these solutions are also symmetric with respect to the direction of propagation.

References

Robert A. Adams, Sobolev spaces, Pure and Applied Mathematics, Vol. 65, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1975. MR 0450957
T. R. Akylas, On the radiation damping of a solitary wave in a rotating channel, Mathematical approaches in hydrodynamics, SIAM, Philadelphia, PA, 1991, pp. 175–181. MR 1136562
Robin Ming Chen, Vera Mikyoung Hur, and Yue Liu, Solitary waves of the rotation-modified Kadomtsev-Petviashvili equation, Nonlinearity 21 (2008), no. 12, 2949–2979. MR 2461048, DOI 10.1088/0951-7715/21/12/012
Wenxiong Chen, Congming Li, and Biao Ou, Classification of solutions for an integral equation, Comm. Pure Appl. Math. 59 (2006), no. 3, 330–343. MR 2200258, DOI 10.1002/cpa.20116
Robin Ming Chen, Yue Liu, and Pingzheng Zhang, Local regularity and decay estimates of solitary waves for the rotation-modified Kadomtsev-Petviashvili equation, Trans. Amer. Math. Soc. 364 (2012), no. 7, 3395–3425. MR 2901218, DOI 10.1090/S0002-9947-2012-05383-9
Anne de Bouard and Jean-Claude Saut, Solitary waves of generalized Kadomtsev-Petviashvili equations, Ann. Inst. H. Poincaré C Anal. Non Linéaire 14 (1997), no. 2, 211–236 (English, with English and French summaries). MR 1441393, DOI 10.1016/S0294-1449(97)80145-X
Anne de Bouard and Jean-Claude Saut, Symmetries and decay of the generalized Kadomtsev-Petviashvili solitary waves, SIAM J. Math. Anal. 28 (1997), no. 5, 1064–1085. MR 1466669, DOI 10.1137/S0036141096297662
Amin Esfahani, Decay properties of the traveling waves of the rotation-generalized Kadomtsev-Petviashvili equation, J. Phys. A 43 (2010), no. 39, 395201, 13. MR 2720059, DOI 10.1088/1751-8113/43/39/395201
Amin Esfahani and Steve Levandosky, Stability of solitary waves of the Kadomtsev-Petviashvili equation with a weak rotation, SIAM J. Math. Anal. 49 (2017), no. 6, 5096–5133. MR 3738307, DOI 10.1137/16M1103865
R. Grimshaw, Evolution equations for weakly nonlinear, long internal waves in a rotating fluid, Stud. Appl. Math. 73 (1985), no. 1, 1–33. MR 797556, DOI 10.1002/sapm19857311
R. Grimshaw, L.A. Ostrovsky, V.I. Shrira, Y.A. Stepanyants, Long nonlinear surface and internal gravity waves in a rotating ocean, Surv. Geophys. 19 (1998) 289–338.
Yan Yan Li, Remark on some conformally invariant integral equations: the method of moving spheres, J. Eur. Math. Soc. (JEMS) 6 (2004), no. 2, 153–180. MR 2055032, DOI 10.4171/jems/6
Yue Liu and Vladimir Varlamov, Stability of solitary waves and weak rotation limit for the Ostrovsky equation, J. Differential Equations 203 (2004), no. 1, 159–183. MR 2070389, DOI 10.1016/j.jde.2004.03.026
P. I. Lizorkin, Multipliers of Fourier integrals and estimates of convolutions in spaces with mixed norm. Applications, Izv. Akad. Nauk SSSR Ser. Mat. 34 (1970), 218–247 (Russian). MR 0262815
T. Maxworthy, Experiments on solitary internal Kelvin waves, J. Fluid Mech. 129 (1983), 365–383.
W. W. Y. Wong, Lecture notes on Sobolev spaces for CCA, http://sma.epfl.ch/\~wwywong/papers/sobolevnotes.pdf.