Multiple Rogue Wave Solutions Research Articles

Multiple rogue wave, double-periodic soliton and breather wave solutions for a generalized breaking soliton system in (3 + 1)-dimensions

We focused on solitonic phenomena in wave propagation which was extracted from a generalized breaking soliton system in (3 + 1)-dimensions. The model describes the interaction phenomena between Riemann wave and long wave via two space variable in nonlinear media. Abundant double-periodic soliton, breather wave and the multiple rogue wave solutions to a generalized breaking soliton system by the Hirota bilinear form and a mixture of exponentials and trigonometric functions are presented. Periodic-soliton, breather wave and periodic are studied with the usage of symbolic computation. In addition, the symbolic computation and the applied methods for governing model are investigated. Through three-dimensional graph, density graph, and two-dimensional design using Maple, the physical features of double-periodic soliton and breather wave solutions are explained all right. The findings demonstrate the investigated model’s broad variety of explicit solutions. All outcomes in this work are necessary to understand the physical meaning and behavior of the explored results and shed light on the significance of the investigation of several nonlinear wave phenomena in sciences and engineering.

Multiple rogue wave solutions for a modified (2 + 1)-dimensional nonlinear evolution equation

Multiple rogue wave solutions for a modified (2 + 1)-dimensional nonlinear evolution equation

Dynamics investigation on a Kadomtsev–Petviashvili equation with variable coefficients

Abstract In this work, we investigate a generalized Kadomtsev–Petviashvili equation with variable coefficients and self-consistent sources in plasma and fluid mechanics. The multiple rogue wave solutions, including 1-, 3-, and 6-order rogue waves, are presented by three different functions under a nonlinear transformation. Based on the Hirota bilinear method and a more complex assumption, new lump solutions are constructed, which have not been seen in other literature. The dynamic properties of the obtained results are illustrated graphically.

Multiple rogue wave solutions of a generalized (3+1)-dimensional variable-coefficient Kadomtsev--Petviashvili equation

Abstract Kadomtsev–Petviashvili equation is used for describing the long water wave and small amplitude surface wave with weak nonlinearity, weak dispersion, and weak perturbation in fluid mechanics. Based on the modified symbolic computation approach, the multiple rogue wave solutions of a generalized (3+1)-dimensional variable-coefficient Kadomtsev–Petviashvili equation are investigated. When the variable coefficient selects different functions, the dynamic properties of the derived solutions are displayed and analyzed by different three-dimensional graphics and contour graphics.

Multiple rational rogue waves for higher dimensional nonlinear evolution equations via symbolic computation approach

The paper investigates the multiple rogue wave solutions associated with the generalized Hirota–Satsuma–Ito (HSI) equation and the newly proposed extended (3 + 1)-dimensional Jimbo–Miwa (JM) equation with the help of a symbolic computation technique. By incorporating a direct variable transformation and utilizing Hirota’s bilinear form, multiple rogue wave structures of different orders are obtained for both generalized HSI and JM equation. The obtained bilinear forms of the proposed equations successfully investigate the 1st, 2nd and 3rd-order rogue waves. The constructed solutions are verified by inserting them into original equations. The computations are assisted with 3D graphs to analyze the propagation dynamics of these rogue waves. Physical properties of these waves are governed by different parameters that are discussed in details.

Multiple rogue wave solutions for the generalized (2+1)-dimensional Camassa–Holm–Kadomtsev–Petviashvili equation

In this work, multiple rogue wave solutions of the generalized (2+1)-dimensional Camassa–Holm–Kadomtsev–Petviashvili equation are studied based on the symbolic computation approach. As an example, we present the 1-rogue wave, 3-rogue wave and 6-rogue wave solutions, which have not been seen in other literature. Furthermore, some dynamic features of the obtained multiple rogue wave solutions are shown by 3D, contour and density graphics.

Characteristics of the new multiple rogue wave solutions to the fractional generalized CBS-BK equation

IntroductionThe multiple Exp-function scheme is employed for searching the multiple soliton solutions for the fractional generalized Calogero-Bogoyavlenskii-Schiff-Bogoyavlensky- Konopelchenko equation. ObjectivesMoreover, the Hirota bilinear technique is utilized to detecting the lump and interaction with two stripe soliton solutions. MethodsThe multiple Exp-function scheme and also, the semi-inverse variational principle will be used for the considered equation. ResultsWe have obtained more than twelve sets of solutions including a combination of two positive functions as polynomial and two exponential functions. The graphs for various fractional-order α are designed to contain three dimensional, density, and y-curves plots. Then, the classes of rogue waves-type solutions to the fractional generalized Calogero-Bogoyavlenskii-Schiff-Bogoyavlensky- Konopelchenko equation within the frame of the bilinear equation, is found. ConclusionFinally, a direct method which is called the semi-inverse variational principle method was used to obtain solitary waves of this considered model. These results can help us better understand interesting physical phenomena and mechanism. The dynamical structures of these gained lump and its interaction soliton solutions are analyzed and indicated in graphs by choosing suitable amounts. The existence conditions are employed to discuss the available got solutions.

Multiple rogue wave solutions of a generalised Hietarinta-type equation

Multiple rogue wave solutions of a generalised Hietarinta-type equation

Multiple rogue wave solutions and the linear superposition principle for a (3 + 1)‐dimensional Kadomtsev–Petviashvili–Boussinesq‐like equation arising in energy distributions

The multiple exp‐function method and multiple rogue wave solutions method are employed for searching the multiple soliton solutions to the (3 + 1)‐dimensional Kadomtsev–Petviashvili–Boussinesq‐like (KP‐Boussinesq‐like) equation. The obtained solutions contain the first‐order, second‐order, third‐order, and fourth‐order wave solutions. At the critical point, the second‐order derivative and Hessian matrix for only one point are investigated, and the lump solution has one maximum value. Moreover, we employ the linear superposition principle to determine N‐soliton wave solutions of the KP‐Boussinesq‐like equation. The physical phenomena of these gained multiple soliton solutions are analyzed and indicated in figures by selecting suitable values.

Modulational instability and multiple rogue wave solutions for the generalized CBS–BK equation

An integrable of the generalized Calogero–Bogoyavlenskii–Schiff–Bogoyavlensky–Konopelchenko (CBS–BK) equation is studied, by employing Hirota’s bilinear method the bilinear form is obtained, and the multiple-soliton solutions are constructed. The modified of improved bilinear method has been utilized to investigate multiple solutions. In addition, some graphs including 3D, contour, density, and [Formula: see text]-curves plots of the addressed equation with specific coefficients are shown. Finally, under certain conditions, the asymptotic behavior of the linearization solution is analyzed to prove that the modulation instability is stable for some points.

Variable-coefficient symbolic computation approach for finding multiple rogue wave solutions of nonlinear system with variable coefficients

In this paper, a variable-coefficient symbolic computation approach is proposed to solve the multiple rogue wave solutions of nonlinear equation with variable coefficients. As an application, a (2+1)-dimensional variable-coefficient Kadomtsev-Petviashvili equation is investigated. The multiple rogue wave solutions are obtained and their dynamics features are shown in some 3D and contour plots.

Resonant multi-soliton and multiple rogue wave solutions of (3+1)-dimensional Kudryashov-Sinelshchikov equation

In this paper, we investigated various exact solutions of (3+1)-dimensional Kudryashov-Sinelshchikov equation in a mixture of liquid and gas bubbles. At first, the linear superposition principle was introduced to obtain resonant multi-soliton solutions and we took two cases as examples to illustrate the wave trajectories and the structure of resonant multi-soliton solutions through several sets of graphs. Next, multiple rogue wave solutions were derived via using the ‘4-2-4’ neural network model and we obtained its 1-rogue wave, 3-rogue wave and 6-rogue wave solutions through symbolic computation. In addition, three-dimensional, contour and density plots of multiple rogue wave solutions vividly shown their physical structure and dynamic properties. Furthermore, these solutions have greatly expanded the exact solutions of (3+1)-dimensional Kudryashov-Sinelshchikov equation on the available literature.

Multiple rogue wave solutions of (2+1)-dimensional YTSF equation via Hirota bilinear method

In present paper, multiple rogue wave solutions of (2+1)-dimensional Yu–Toda–Sasa–Fukuyama equation were studied by applying the traveling wave transformation and the Hirota bilinear method. We obtained its 1-rogue wave, 3-rogue wave, 6-rogue wave and 8-rogue wave solutions through symbolic computation. Three-dimensional, contour and density plots of corresponding solutions vividly shown the physical structure and properties. Furthermore, these solutions have greatly enriched the exact solutions of (2+1)-dimensional Yu–Toda–Sasa–Fukuyama equation on the existing literature.

Multiple rogue wave, dark, bright, and solitary wave solutions to the KP–BBM equation

Under investigation in this paper is the (2+1)-dimensional Kadomtsev–Petviashvili–Benjamin–Bona–Mahony equation. Based on bilinear method, the multiple rogue wave solutions and the novel multiple soliton solutions are constructed by giving some specific activation functions in the considered model. By means of symbolic computation, these analytical solutions and corresponding rogue waves are obtained, via Maple 18. By utilizing improved tan(Φ(ρ)∕2)-expansion technique the series of novel exact solutions in terms of rational, periodic and hyperbolic functions for the fractional cases are derived. Also, the semi-inverse variational principle is offered to get the solitary solutions. We construct the exact lump and rogue wave solutions, by solving the under-determined nonlinear system of algebraic equations for the specified parameters. Via various three-dimensional plots, curve plots, density plots and contour plots, dynamical characteristics of these waves are represented.

Breathers and multiple rogue waves solutions of the (3+1)-dimensional Jimbo–Miwa equation

In this paper, we construct the breathers of the (3+1)-dimensional Jimbo–Miwa (JM) equation by means of the Hirota bilinear method, then based on the Hirota bilinear method with a new ansatz form, the multiple rogue wave solutions are constructed. Here, we discuss the general breathers, first-order rogue waves, the second-order rogue waves and the third-order rogue waves. Then we draw the 3- and 2-dimensional plots to illustrate the dynamic characteristics of breathers and multiple rogue waves. These interesting results will help us better reveal (3+1)-dimensional JM equation evolution mechanism.

Multiple rogue wave, breather wave and interaction solutions of a generalized (3 + 1)-dimensional variable-coefficient nonlinear wave equation

Based on a direct variable transformation, we obtain multiple rogue wave solutions of a generalized (3 + 1)-dimensional variable-coefficient nonlinear wave equation, including first-order, two-order and three-order rogue wave solutions. Their dynamic behaviors are shown by some 3D plots. Compared with Zha’s symbolic computation approach, we do not need to resort to Hirota bilinear form, and it can be used to deal with variable-coefficient integrable equations. Interaction solution between rogue wave and periodic wave is obtained by using the Hirota bilinear form. Abundant breather wave solutions are presented by a direct test function.

Multiple rogue wave, lump‐periodic, lump‐soliton, and interaction betweenk‐lump andk‐stripe soliton solutions for the generalized KP equation

The multiple rogue wave solutions technique is engaged to seek the multifold soliton solutions for the generalized (2 + 1)‐dimensional Kadomtsev–Petviashvili (gKP) equation, which contains one wave, two waves, and triple waves solutions. The second‐order derivative will be perused to get the minimum or maximum amount of lump solution. For one case, the lump solution will be shown the bright‐dark lump structure, and for another case, the dark lump structure two small peaks and one deep hole can be present. Also, the interaction of lump with periodic waves and the interaction between the lump and two stripe solitons can be catched by introducing the Hirota forms. Simultaneously, the interaction betweenk‐lump andk‐stripe soliton wave solutions can be gained by the Hirota operator. The physical phenomena of these gained multiple soliton solutions are analyzed and indicated in diagrams by choosing proper amounts.

Multiple rogue wave solutions for a variable-coefficient Kadomtsev–Petviashvili equation

The multiple rogue wave solutions method is employed for searching the multiple soliton solutions for the new variable-coefficient Kadomtsev–Petviashvili equation, which contains first-order, second-order, third-order, and fourth-order wave solutions. At the critical point, the second-order derivative and Hessian matrix for only one point will be investigated and the lump solution has one maximum value. The physical phenomena of these gained multiple soliton solutions are analysed and indicated in figures by selecting suitable values.

Multiple rogue wave solutions for (2+1)-dimensional Boussinesq equation

In this paper, a modified symbolic computation approach is proposed. The multiple rogue wave solutions of a generalized (2+1)-dimensional Boussinesq equation are obtained by using the modified symbolic computation approach. Dynamics features of these obtained multiple rogue wave solutions are displayed in 3D and contour plots. Compared with the original symbolic computation approach, our method does not need to find Hirota bilinear form of nonlinear system.

Analysis on the M-rogue wave solutions of a generalized (3+1)-dimensional KP equation

In this paper, multiple rogue wave solutions of a generalized (3+1)-dimensional Kadomtsev–Petviashvili (KP) equation are studied. Based on the bilinear form of this considered equation and a generalized ansatz form, the N-order rogue waves can be constructed. Here we only show in the first-order rogue waves, the second-order rogue waves and the third-order rogue waves. Then, dynamic characteristics of multiple rogue waves are analyzed by drawing the 3D-and 2D-dimensional plots. We see that the M-rogue wave consists of M-independent single first order rogue wave. This interesting phenomenon can help us better reveal KP equation evolution mechanism.