References
- Isaza P, Mejia J. Local and global Cauchy problems for the Kadomtsev-Petviashvili (KP-II) equation in Sobolev spaces of negative indices. Comm Partial Differ Equ. 2001;26:1027–1054.
- Ablowitz MJ, Clarkson PA. Solitons, nonlinear evolution equations and inverse scattering. Cambridge: Cambridge University Press; 1991.
- Groves MD, Sun S-M. Fully localised solitary-wave solutions of the three-dimensional gravity-capillary water-wave problem. Arch Ration Mech Anal. 2008;188:1–91.
- Hammack J, McCallister D, Scheffner N, et al. Two-dimensional periodic waves in shallow water. II. asymmetric waves. J Fluid Mech. 1995;285:95–122.
- Segur H, Finkel A. An analytical model of periodic waves in shallow water. Stud Appl Math. 1985;73:183–220.
- de Bouard A, Saut J-C. Sur les ondes solitaires des équations de Kadomtsev-Petviashvili. C R Acad Sci Paris Sér I Math. 1995;320:315–318.
- de Bouard A, Saut J-C. Solitary waves of generalized Kadomtsev-Petviashvili equations. Ann Inst H Poincaré C Anal Non Linéaire. 1997;14:211–236.
- Lions P-L. The concentration-compactness principle in the calculus of variations. the locally compact case I. Ann Inst H Poincaré Anal Non Linéaire. 1984;1:109–145.
- Willem M. Minimax theorems. Boston: Birkhäuser; 1996.
- Rabinowitz PH. Minimax methods in critical point theory with applications to differential equations. Providence (RI): American Mathematical Society; 1986.
- Wang Z-Q, Willem M. A multiplicity result for the generalized Kadomtsev-Petviashvili equation. Topol Methods Nonlinear Anal. 1996;7:261–270.
- Liang ZP, Su JB. Existence of solitary waves to a generalized Kadomtsev-Petviashvili equation. Acta Math Sci Ser B. 2012;32:1149–1156.
- Xuan BJ. Nontrivial solitary waves of GKP equation in multi-dimensional spaces. Rev Colombiana Mat. 2003;37:11–23.
- He XM, Zou WM. Nontrivial solitary waves to the generalized Kadomtsev-Petviashvili equations. Appl Math Comput. 2008;197:858–863.
- Alves CO, Ji C. Existence and concentration of nontrivial solitary waves for a generalized Kadomtsev–Petviashvili equation in R2. 2022, arXiv:2209.12214.
- Bourgain J. On the Cauchy problem for the Kadomtsev-Petviashvili equation. Geom Funct Anal. 1993;3:315–341.
- Faminskii AV. The Cauchy problem for the Kadomtsev-Petviashvili equation. Russian Math Surveys. 1990;45:203–204.
- Figueiredo G, Montenegro M. Multiple solitary waves for a generalized Kadomtsev-Petviashvili equation with a potential. J Differ Equ. 2022;308:40–56.
- Hayashi N, Naumkin PI, Saut J-C. Asymptotics for large time of global solutions to the generalized Kadomtsev-Petviashvili equation. Comm Math Phys. 1999;201:577–590.
- Kadomtsev BB, Petviashvili VI. On the stability of solitary waves in weakly dispersing media. Soviet Physics. Dokl; 1970;15:539–541.
- Saut J-C. Recent results on the generalized Kadomtsev-Petviashvili equations. Acta Appl Math. 1995;39:477–487.
- Tzvetkov N. Global low-regularity solutions for Kadomtsev-Petviashvili equation. Differ Int Equ. 2000;13:1289–1320.
- Xuan BJ. Nontrivial stationary solutions to GKP equation in bounded domain. Appl Anal. 2003;82:1039–1048.
- Zou WM. Solitary waves of the generalized Kadomtsev-Petviashvili equations. Appl Math Lett. 2002;15:35–39.
- Alves CO, Miyagaki OH, Pomponio A. Solitary waves for a class of generalized Kadomtsev-Petviashvili equation in RN with positive and zero mass. J Math Anal Appl. 2019;477:523–535.
- Szulkin A, Weth T. Ground state solutions for some indefinite variational problems. J Funct Anal. 2009;257:3802–3822.
- Besov OV, II'in VP, Nikol'skii SM. Integral representations of functions and imbedding theorems. Vol. I. New York: John Wiley & Sons; 1978.