The rogue wave solutions of a new (2+1)-dimensional equation

Qiu, Deqin; Zhang, Yongshuai; He, Jingsong

doi:10.1016/j.cnsns.2015.06.025

Cited by 47 publications

(28 citation statements)

References 53 publications

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“…It is also used to address the problems of hole waves and oceanic rogue waves [30]. The model can further find to be applicable to the study of soliton pulses occurring in (2+1)-dimensional equations [31]. The most important feature of this model is that it has been given as a new extension of nonlinear Schrödinger (NLS) equation with the inclusion of different forms of nonlinearity with regard to Kerr and non-Kerr law nonlinearities to study soliton pulses in (2+1)-dimensions [31,32].…”

Section: Background and Literature Reviewmentioning

confidence: 99%

Optical solutions to the Kundu-Mukherjee-Naskar equation: mathematical and graphical analysis with oblique wave propagation

Kumar

Paul

Biswas

et al. 2020

Preprint

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This paper retrieves some new optical solutions to the Kundu-Mukherjee-Naskar (KMN) equation in the context of nonlinear optical fiber communication systems. In this regard, the generalized Kudryashov and new auxiliary equation methods are applied to the KMN equation and consequently, dark, bright, periodic U-shaped and singular soliton solutions are explored. The discrepancies between the present obtained solutions and the previously obtained solutions by using different methods are discussed. The time fractional derivative and an oblique wave transformation in coordination with the methods of interest are considered for acquiring new optical wave solutions of the KMN equation in the sense of conformable derivative and wave obliqueness, respectively. The effects of obliqueness and fractionality on the attained solutions are demonstrated graphically along with its physical descriptions. It is found that the optical wave phenomena are changed with the increase of obliqueness as well as fractionality. All the obtained optical solutions are found to be new in the sense of conformable derivative, wave obliqueness, and the applied methods. Finally, it is found that the utilized methods and the relevant transformation are powerful over the other methods and it can be applicable for further studies to explain the pragmatic phenomena in optical fiber communication systems.

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Section: Background and Literature Reviewmentioning

confidence: 99%

Optical solutions to the Kundu-Mukherjee-Naskar equation: mathematical and graphical analysis with oblique wave propagation

Kumar

Paul

Biswas

et al. 2020

Preprint

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“…At present the contour line method is really a useful tool to analyse the localization characters at a given height c 2 + 1 (i.e. d = 1) of the first-order RW solution [23,[36][37][38]. In the following context we shall use contour line of |u [1] rw | 2 with given values of parameters (a, c, β) to study the evolution of profile with a varying d. By this method, a contour line of |u [1] rw | 2 at height c 2 + d (d > 0) along the orthogonal direction of the (t, x)-plane is expressed by…”

Section: The Critical Height D Cmentioning

confidence: 99%

“…Especially, the squared modulus of the solution |u| 2 always represents a measurable quantity, optical power (or intensity). Recently, a effective tool, contour line method, is applied to study the localization characters of the profile for rogue waves by computing the width, length and area [23,[36][37][38]. It is known that the contour line on the asymptotic plane is a hyperbola, while the contour line above the asymptotic plane is a closed curve and then the width, length and area of the rogue wave can be worked out [23].…”

Section: Introductionmentioning

confidence: 99%

“…It is known that the contour line on the asymptotic plane is a hyperbola, while the contour line above the asymptotic plane is a closed curve and then the width, length and area of the rogue wave can be worked out [23]. But in [23,[36][37][38], we just analysed the localization characters at a given height c 2 + 1 along the orthogonal direction of the (t, x)-plane, where c 2 is the height of asymptotic background for rogue wave |u| 2 . How does these localized characters are evolving along the orthogonal direction of the (t, x)-plane ?…”

Section: Introductionmentioning

confidence: 99%

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On the evolution of a rogue wave along the orthogonal direction of the (t, x)-plane

Yuan

Qiu

Liu³

et al. 2017

Communications in Nonlinear Science and Numerical Simulation

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Abstract. The localization characters of the first-order rogue wave (RW) solution u of the Kundu-Eckhaus equation is studied in this paper. We discover a full process of the evolution for the contour line with height c 2 + d along the orthogonal direction of the (t, x)-plane for a first-order RW |u| 2 : A point at height 9c 2 generates a convex curve for 3c 2 ≤ d < 8c 2 , whereas it becomes a concave curve for 0 < d < 3c2 , next it reduces to a hyperbola on asymptotic plane (i.e. equivalently d = 0), and the two branches of the hyperbola become two separate convex curves when −c 2 < d < 0, and finally they reduce to two separate points at d = −c 2 . Using the contour line method, the length, width, and area of the RW at height2 ) , i.e. above the asymptotic plane, are defined. We study the evolutions of three above-mentioned localization characters on d through analytical and visual methods. The phase difference between the Kundu-Eckhaus and the nonlinear Schrodinger equation is also given by an explicit formula.

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“…We obtain the explicit Hirota bilinear form and the general N -soliton solutions, breather, and rational solutions are given. An effective tool, namely the contour line method is applied to study the localization characteristics of the profiles of the obtained RWs [62,[83][84][85][86]. It is well known that the contour line above the asymptotic plane is a closed curve, while the contour line on the asymptotic plane is a hyperbola.…”

Section: Introductionmentioning

confidence: 99%

Families of exact solutions of a new extended $$\varvec{(2+1)}$$(2+1)-dimensional Boussinesq equation

Cao

Mihalache

2018

Nonlinear Dyn

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A new variant of the (2 + 1)-dimensional [(2 + 1)d] Boussinesq equation was recently introduced by J. Y. Zhu, arXiv:1704.02779v2, 2017; see eq. (3). First, we derive in this paper the one-soliton solutions of both bright and dark types for the extended (2 + 1)d Boussinesq equation by using the traveling wave method. Second, N -soliton, breather, and rational solutions are obtained by using the Hirota bilinear method and the long wave limit. Nonsingular rational solutions of two types were obtained analytically, namely: (i) rogue-wave solutions having the form of W-shaped lines waves and (ii) lump-type solutions. Two generic types of semi-rational solutions were also put forward. The obtained semi-rational solutions are as follows: (iii) a hybrid of a first-order lump and a bright one-soliton solution and (iv) a hybrid of a first-order lump and a first-order breather.

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The rogue wave solutions of a new (2+1)-dimensional equation

Cited by 47 publications

References 53 publications

Optical solutions to the Kundu-Mukherjee-Naskar equation: mathematical and graphical analysis with oblique wave propagation

Optical solutions to the Kundu-Mukherjee-Naskar equation: mathematical and graphical analysis with oblique wave propagation

On the evolution of a rogue wave along the orthogonal direction of the (t, x)-plane

Families of exact solutions of a new extended $$\varvec{(2+1)}$$(2+1)-dimensional Boussinesq equation

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