Dynamical interactions between higher-order rogue waves and various forms of n-soliton solutions (n → ∞) of the (2+1)-dimensional ANNV equation

doi:10.1088/1674-1056/aba612

Abstract

We present new lemmas, theorem and corollaries to construct interactions among higher-order rogue waves, n-periodic waves and n-solitons solutions (n → ∞) to the (2+1)-dimensional asymmetric Nizhnik–Novikov–Veselov (ANNV) equation. Several examples for theories are given by choosing definite interactions of the wave solutions for the model. In particular, we exhibit dynamical interactions between a rogue and a cross bright-dark bell wave, a rogue and a cross-bright bell wave, a rogue and a one-, two-, three-, four-periodic wave. In addition, we also present multi-types interactions between a rogue and a periodic cross-bright bell wave, a rogue and a periodic cross-bright-bark bell wave. Finally, we physically explain such interaction solutions of the model in the 3D and density plots.

Keywords: the (2+1)-dimensional asymmetric Nizhnik-Novikov-Veselov (ANNV) equation higher-order rogue waves n-solitons periodic waves bright-dark bell waves

Received: 01 June 2020
Revised: 06 July 2020
Accepted manuscript online: 15 July 2020

Corresponding Authors: ^†Corresponding author. E-mail: fazlul_math@yahoo.co.in; f.alshammari@psau.edu.sa ^‡Corresponding author. E-mail: harunorroshidmd@gmail.com

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Md Fazlul Hoque, Harun-Or-Roshid, and Fahad Sameer Alshammari Dynamical interactions between higher-order rogue waves and various forms of n-soliton solutions (n → ∞) of the (2+1)-dimensional ANNV equation 2020 Chin. Phys. B 29 114701

Fig. 1.

The 3D (upper) and density (lower) profiles of Eq. (8) for ${\mathscr{W}}$: interaction between (a) a rogue and a bright bell wave, (b) a rogue and a two-bell (one bright and one dark) wave, and (c) a rogue and a four-bell (double bright and double dark) wave.

Fig. 2.

The 3D (upper) and density (lower) profiles of Eq. (8) for ${\mathscr{V}}$: interaction between (a) a rogue and a bright bell wave, (b) a rogue and a two-cross-bright-bell wave, and (c) a rogue and a four-cross-bright-bell wave.

Fig. 3.

The 3D (upper) and density (lower) profiles of Eq. (17) for ${\mathscr{W}}$: (a) a single rogue wave; and interaction between (b) a rogue and a bright bell wave, and (c) a rogue and a three-bell (double bright and single dark) wave.

Fig. 4.

The 3D (upper) and density (lower) profiles of Eq. (17) for ${\mathscr{V}}$: (a) a single rogue wave; and interaction between (b) a rogue and a cross-bright bell wave, and (c) a rogue and a triple cross-bright bell wave.

Fig. 5.

The 3D (upper) and density (lower) profiles of Eq. (18) for ${\mathscr{W}}$: interaction between (a) a rogue and a periodic wave, (b) a rogue and a double periodic wave, and (c) a rogue and a triple periodic wave.

Fig. 6.

The 3D (upper) and density (lower) profiles of Eq. (18) for ${\mathscr{V}}$: interaction between (a) a rogue and a periodic wave, (b) a rogue and a double periodic wave, and (c) a rogue and a triple periodic wave.

Fig. 7.

The 3D (upper) and density (lower) profiles of Eq. (19) for ${\mathscr{W}}$: interaction between (a) a rogue and a periodic wave, (b) a rogue and a double periodic wave, and (c) a rogue and a four-periodic-bell wave.

Fig. 8.

The 3D (upper) and density (lower) profiles of Eq. (19) for ${\mathscr{V}}$: interaction between (a) a rogue and a periodic wave, (b) a rogue and a double-periodic-bell wave, and (c) a rogue and a four-periodic-bell wave.

Fig. 9.

The 3D (upper) and density (lower) profiles of Eq. (20) for ${\mathscr{W}}$: multi-interaction among a rogue periodic wave and bright-bark bell soliton waves.

Fig. 10.

The 3D (upper) and density (lower) profiles of Eq. (20) for ${\mathscr{V}}$: multi-interaction among a rogue periodic wave and bright-bark bell soliton waves.

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Dynamical interactions between higher-order rogue waves and various forms of n-soliton solutions (n → ∞) of the (2+1)-dimensional ANNV equation

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