Rogue waves, homoclinic breather waves and soliton waves for the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="mml18" display="inline" overflow="scroll" altimg="si18.gif"><mml:mrow><mml:mo>(</mml:mo><mml:mn>2</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math>-dimensional B-type Kadomtsev–Petviashvili equation

Feng, Lian-Li; Tian, Shou‐Fu; Wang, Xiu‐Bin; Zhang, Tiantian

doi:10.1016/j.aml.2016.10.009

Cited by 98 publications

(11 citation statements)

References 30 publications

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“…A growing interest has been given to the KdV6 equation as an example for the propagation of nonlinear waves in nonlinear dynamical fields and confirming its integrability. It was also proved that the KdV6 equation is equivalent to the Rosochatius deformation of the KdV equation with self-consistent sources (Feng et al , 2017; Khalique, 2013; Wazwaz, 2008, 2015, 2016, 2017). Lax pairs and infinite conservation laws were obtained in Feng et al (2017), Khalique (2013), Wazwaz (2008, 2015, 2016, 2017) and some of the references there in.…”

Section: Introductionmentioning

confidence: 97%

“…The KdV6 equation was established using the equation: where the second factor in equation (1) is the potential KdV equation (Feng et al , 2017; Khalique, 2013; Wazwaz, 2008, 2015, 2016, 2017). However, the Painlevé analysis was used to test the complete integrability of the sixth-order nonlinear equation (KdV6), given by: where a , b , c , d , e , f and g are arbitrary parameters, where there are four distinct cases of relations between the parameters when equation (2) passes the Painlevé test well.…”

Section: Introductionmentioning

confidence: 99%

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An extended time-dependent KdV6 equation

Wazwaz

2019

HFF

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Purpose The purpose of this paper is to develop a new time-dependent KdV6 equation. The authors derive multiple soliton solutions and multiple complex soliton solutions for a time-dependent equation. Design/methodology/approach The newly developed time-dependent model has been handled by using the Hirota’s direct method. The authors also use the complex Hirota’s criteria for deriving multiple complex soliton solutions. Findings The examined extension of the KdV6 model exhibits complete integrability for any analytic time-dependent coefficient. Research limitations/implications The paper presents a new efficient algorithm for constructing extended models which give a variety of multiple real and complex soliton solutions. Practical implications The paper introduced a new time-dependent KdV6 equation, where integrability is emphasized for any analytic time-dependent function. Social implications The findings are new and promising. Multiple real and multiple complex soliton solutions were formally derived. Originality/value This is an entirely new work where a new time-dependent KdV6 equation is established. This is the first time that the KdV6 equation is examined as a time-dependent equation. Moreover, the complete integrability of this newly developed equation is emphasized via using Painlevé test.

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Section: Introductionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

An extended time-dependent KdV6 equation

Wazwaz

2019

HFF

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“…ough different from tsunami, the rogue waves that occur in the ocean have extraordinary destructiveness. Recently, rogue waves especially optical ones gained high attention [2][3][4][5][6][7][8][9][10][11][12][13][14]. It is Solli et al [2] who reported the optical rogue waves generated through a generalized NLS equation.…”

Section: Introductionmentioning

confidence: 99%

Fractional Rogue Waves with Translational Coordination, Steep Crest, and Modified Asymmetry

Zhang

2021

Complexity

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To construct fractional rogue waves, this paper first introduces a conformable fractional partial derivative. Based on the conformable fractional partial derivative and its properties, a fractional Schrödinger (NLS) equation with Lax integrability is then derived and first- and second-order fractional rogue wave solutions of which are finally obtained. The obtained fractional rogue wave solutions possess translational coordination, providing, to some extent, the degree of freedom to adjust the position of the rogue waves on the coordinate plane. It is shown that the obtained first- and second-order fractional rogue wave solutions are steeper than those of the corresponding NLS equation with integer-order derivatives. Besides, the time the second-order fractional rogue wave solution undergoes from the beginning to the end is also short. As for asymmetric fractional rogue waves with different backgrounds and amplitudes, this paper puts forward a way to construct them by modifying the obtained first- and second-order fractional rogue wave solutions.

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“…But it was originally used to describe a particular wave that appeared in the ocean (Müller et al, 2005). More recently, there have been many works to investigate rogue wave solutions for NLEEs (Feng et al, 2019;Mao et al, 2018;Guo et al, 2019;Peng et al, 2019b;Feng and Zhang, 2018;Wang et al,2018a;Xu et al, 2014;Ohta and Yang, 2012;Bayindir, 2016;He et al, 2012;Dong et al, 2018aDong et al, , 2018bWang et al, 2018bWang et al, , 2018cPeng et al, 2018a;Yan et al, 2018aYan et al, , 2018bPeng et al, 2018b;Tian, 2018aTian, , 2018bWang and Tian, 2018;Tian, 2019aTian, , 2019bWang et al, 2016a;Feng et al, 2017).…”

Section: Introductionmentioning

confidence: 99%

Characteristics of the breather waves, rogue waves and solitary waves in an extended (3 + 1)-dimensional Kadomtsev–Petviashvili equation

Wang

Tian

2019

HFF

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Purpose The purpose of this paper is to study the breather waves, rogue waves and solitary waves of an extended (3 + 1)-dimensional Kadomtsev–Petviashvili (KP) equation, which can be used to depict many nonlinear phenomena in fluid dynamics and plasma physics. Design/methodology/approach The authors apply the Bell’s polynomial approach, the homoclinic test technique and Hirota’s bilinear method to find the breather waves, rogue waves and solitary waves of the extended (3 + 1)-dimensional KP equation. Findings The results imply that the extended (3 + 1)-dimensional KP equation has breather wave, rogue wave and solitary wave solutions. Meanwhile, the authors provide the graphical analysis of such solutions to better understand their dynamical behavior. Originality/value These results may help us to further study the local structure and the interaction of solutions in KP-type equations. The authors hope that the results provided in this work can help enrich the dynamic behavior of such equations.

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Rogue waves, homoclinic breather waves and soliton waves for the (2+1)-dimensional B-type Kadomtsev–Petviashvili equation

Cited by 98 publications

References 30 publications

An extended time-dependent KdV6 equation

An extended time-dependent KdV6 equation

Fractional Rogue Waves with Translational Coordination, Steep Crest, and Modified Asymmetry

Characteristics of the breather waves, rogue waves and solitary waves in an extended (3 + 1)-dimensional Kadomtsev–Petviashvili equation

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