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

Md Fazlul Hoque^{1, †}, Harun-Or-Roshid^{1,, ‡}, and Fahad Sameer Alshammari^{2}

1 Department of Mathematics, Pabna University of Science and Technology, Pabna 6600, Bangladesh 2 Department of Mathematics, College of Science at Alkharj, Prince Sattam bin Abdulaziz University, Alkharj, Saudi Arabia

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.

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.

Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.