Interaction of multi-lumps within the Kadomtsev–Petviashvili equation

Kadomtsev, 1970, On the stability of solitary waves in weakly dispersing media, Sov. Phys. Dokl., 15, 539

Petviashvili, 1992

Ablowitz, 1981

Ablowitz, 1991

Hirota, 1980, 157

Matveev, 1991

Potapov, 1984, Quasi-plane beam of nonlinear longitudinal waves in a plate, Sov. Phys. Acoust., 30, 486

Pelinovsky, 1995, Self-focusing of plane dark solitons in nonlinear defocusing media, Phys. Rev. E, 51, 5016, 10.1103/PhysRevE.51.5016

Porubov, 2004, Localization of two-dimensional non-linear strain waves in a plate, Int. J. Non-Linear Mech., 39, 1359, 10.1016/j.ijnonlinmec.2003.12.002

Grimshaw, 2015, Effect of a background shear current on models for nonlinear long internal waves, Fundam. Appl. Hydrophys., 8, 20

Singh, 2016, Obliquely propagating skew KP lumps, Wave Motion, 64, 92, 10.1016/j.wavemoti.2016.03.005

Petviashvili, 1976, Equation of an extraordinary soliton, Fiz. Plazmy, 2, 469

Manakov, 1977, Two-dimensional solitons of the Kadomtsev-Petviashvili equation and their interaction, Phys. Lett. A, 63, 205, 10.1016/0375-9601(77)90875-1

Satsuma, 1979, Two-dimensional lumps in nonlinear dispersive systems, J. Math. Phys., 20, 1496, 10.1063/1.524208

Lu, 2004, Interaction of two lump solitons described by the KadomtsevPetviashvili I equation, Wave Motion, 40, 123, 10.1016/j.wavemoti.2003.12.017

Ma, 2015, Lump solutions to the Kadomtsev–Petviashvili equation, Phys. Lett. A, 379, 1975, 10.1016/j.physleta.2015.06.061

Gorshkov, 1993, Normal and anomalous scattering, formation and decay of bound states of two-dimensional solitons described by the Kadomtsev-Petviashvili equation, JETP, 77, 237

Abramyan, 1985, Two-dimensional multisolitons: Stationary solutions of Kadomtsev–Petviashvili equation, Radiophys. Quantum Electron., 28, 20, 10.1007/BF01037453

Pelinovsky, 2004, Convergence of Petviashvili’s iteration method for numerical approximation of stationary solutions of nonlinear wave equations, SIAM J. Numer. Anal., 42, 1110, 10.1137/S0036142902414232

Pelinovsky, 1993, New multisoliton solutions of the Kadomtsev–Petviashvili equation, JETP Lett., 57, 24

Kuznetsov, 1982, Two- and three-dimensional solitons in weakly dispersive media, Sov. Phys.—JETP, 1457

Minzoni, 1996, Evolution of lump solutions for the KP equation, Wave Motion, 24, 291, 10.1016/S0165-2125(96)00023-6

Pelinovsky, 1993, Self-focusing instability of plane solitons and chains of two-dimensional solitons in positive-dispersion media, JETP, 77, 602

Infeld, 1995, Numerical simulations of Kadomtsev-Petviashvili soliton interactions, Phys. Rev. E, 51, 3183, 10.1103/PhysRevE.51.3183

Hu, 2017, The generation of symmetric and asymmetric lumps by a bottom topography, Wave Motion, 75, 62, 10.1016/j.wavemoti.2017.07.006

Lu, 2005, The generation of lump solitons by a bottom topography in a surface-tension dominated flow, Z. Naturforsch. A, 60, 328, 10.1515/zna-2005-0504

Berger, 2000, The generation and evolution of lump solitary waves in surface-tension-dominated flows, SIAM J. Appl. Math., 61, 731, 10.1137/S0036139999356971

Părău, 2005, Three-dimensional gravity-capillary solitary waves in water of finite depth and related problems, Phys. Fluids, 17, 99, 10.1063/1.2140020

Kim, 2005, On gravity-capillary lumps, J. Fluid Mech., 540, 337, 10.1017/S0022112005005823

Kim, 2006, On gravity-capillary lumps. Part 2. Two-dimensional Benjamin equation, J. Fluid Mech., 557, 237, 10.1017/S0022112006009773

W.X. Ma, Y. Zhou, Lump solutions to nonlinear partial differential equations via Hirota bilinear forms, ArXiv e-prints nlin.SI, 2016.

Stepanyants, 2017, Multi-Lump Structures in the Kadomtsev–Petviashvili Equation, 307

Feng, 1998, A finite difference method for the Korteweg-de Vries and the Kadomtsev-Petviashvili equations, J. Comput. Appl. Math., 90, 95, 10.1016/S0377-0427(98)00006-5

Villarroel, 1999, On the discrete spectrum of the nonstationary Schrödinger equation and multipole lumps of the Kadomtsev–Petviashvili I equation, Comm. Math. Phys., 207, 1, 10.1007/s002200050716

W. Hu, W. Huang, Z. Lu, Y. Stepanyants, Animation of lump interactions within the framework of KP1 equation, 2017.

Karpman, 1975

Gaillard, 2016, Rational solutions to the KPI equation and multi rogue waves, Ann. Physics, 367, 1, 10.1016/j.aop.2016.01.013