New Horizons in Mathematical Physics
Families of Solutions of Order 5 to the Johnson Equation Depending on 8 Parameters
Download PDF (1755.2 KB) PP. 53 - 61 Pub. Date: December 1, 2018
Author(s)
- Pierre Gaillard*
Université de Bourgogne, Institut de mathématiques de Bourgogne, 9 avenue Alain Savary BP 47870 - 21078 Dijon Cedex, France
Abstract
Keywords
References
[1] R.E. Johnson, Water waves and Korteweg?de Vries equations, J. Fluid Mech., V. 97, N. 4, 701?719, 1980
[2] R.E. Johnson, A Modern Introduction to the Mathematical Theory of Water Waves, Cambridge University Press, Cambridge, 1997
[3] M. J. Ablowitz, Nonlinear Dispersive Waves : Asymptotic Analysis and Solitons, Cambridge University Press, Cambridge, 2011
[4] V.D. Lipovskii1, On the nonlinear internal wave theory in fluid of finite depth, Izv. Akad. Nauka., V. 21, N. 8, 864?871, 1985
[5] B.B. Kadomtsev, V.I. Petviashvili, On the stability of solitary waves in weakly dispersing media, Sov. Phys. Dokl., V. 15, N. 6, 539-541, 1970
[6] V.I. Golin?ko, V.S. Dryuma, Yu.A. Stepanyants, Nonlinear quasicylindrical waves: Exact solutions of the cylindrical Kadomtsev- Petviashvili equation, in Proc. 2nd Int. Workshop on Nonlinear and Turbulent Processes in Physics, Kiev, Harwood Acad., Gordon and Breach, 1353?1360, 1984
[7] V.D. Lipovskii, V.B. Matveev, A.O. Smirnov, Connection between the Kadomtsev-Petvishvili and Johnson equation, Zap. Nau. Sem., V. 150, 70?75, 1986
[8] C. Klein, V.B. Matveev, A.O. Smirnov, Cylindrical Kadomtsev-Petviashvili equation: Old and new results, Theor. Math. Phys., V. 152, N. 2, 1132-1145, 2007
[9] K. R. Khusnutdinova, C. Klein, V.B. Matveev, A.O. Smirnov, On the integrable elliptic cylindrical K-P equation Chaos, V. 23, 013126-1-15, 2013
[10] P. Gaillard, Families of quasi-rational solutions of the NLS equation and multi-rogue waves, J. Phys. A : Meth. Theor., V. 44, 1-15, 2010
[11] P. Gaillard, Degenerate determinant representation of solution of the NLS equation, higher Peregrine breathers and multi-rogue waves, Jour. Of Math. Phys., V. 54, 2013, 013504-1-32
[12] P. Gaillard, Multi-parametric deformations of the Peregrine breather of order N solutions to the NLS equation and multi-rogue waves, Adv. Res., V. 4, 2015, pp-346-364
[13] P. Gaillard, Fredholm and Wronskian representations of solutions to the KPI equation and multi-rogue waves, Jour. of Math. Phys., V. 57, 063505-1-13, 2016
[14] P. Gaillard, Multiparametric families of solutions of the KPI equation, the structure of their rational representations and multi-rogue waves, Theo. And Mat. Phys., V. 196, N. 2, 1174-1199, 2018