Solitary waves, homoclinic breather waves and rogue waves of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="mml19" display="inline" overflow="scroll" altimg="si19.gif"><mml:mrow><mml:mo>(</mml:mo><mml:mn>3</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math>-dimensional Hirota bilinear equation

Dong, Ming; Tian, Shou‐Fu; Yan, Xue-Wei; Zou, Li

doi:10.1016/j.camwa.2017.10.037

Cited by 99 publications

(20 citation statements)

References 46 publications

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“…It is also integrable by the one-dimensional inverse scattering transform and Painléve test [28][29][30][31]. Recently, more and more people are interested in studying some generalized nonlinear evolution equations [32][33][34][35][36][37][38], resulting from their more widely applications in many physical fields [39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54]. To our knowledge, Riemann theta function periodic wave solutions for Eq.…”

Section: Introductionmentioning

confidence: 99%

Solitary Wave and Quasi-Periodic Wave Solutions to a (3+1)-Dimensional Generalized Calogero-Bogoyavlenskii-Schiff Equation

Qin¹

2018

AAMM

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A (3+1)-dimensional generalized Calogero-Bogoyavlenskii-Schiff equation is considered, which can be used to describe many nonlinear phenomena in plasma physics. By virtue of binary Bell polynomials, a bilinear representation of the equation is succinctly presented. Based on its bilinear formalism, we construct soliton solutions and Riemann theta function periodic wave solutions. The relationships between the soliton solutions and the periodic wave solutions are strictly established and the asymptotic behaviors of the Riemann theta function periodic wave solutions are analyzed with a detailed proof.

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Section: Introductionmentioning

confidence: 99%

Solitary Wave and Quasi-Periodic Wave Solutions to a (3+1)-Dimensional Generalized Calogero-Bogoyavlenskii-Schiff Equation

Qin¹

2018

AAMM

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“…where 1 , e i 1 are given by (14). Similarly, taking N = 2, the two periodic wave solutions for Equation (4) have the following form u = g = 1 + e 1 +i 1 + e 2 +i 2 + e 1 + 2 +i 1 +i 2 +A 12 1 + e 1 + e 2 + e 1 + 2 +A 12 ,…”

Section: Soliton Solutionsmentioning

confidence: 99%

“…Recently, many attentions have been focused on the research of breathers, rogue waves, and lump waves. [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] Lump and rogue waves, both are rational solutions, are observed in many physical phenomena, such as nonlinear optic media, superfluids and Bose-Einstein condensates, and so on. [22][23][24][25][26][27][28][29] In addition, searching for semi-rational solutions of NLEEs also has caused concern for scientists.…”

Section: Introductionmentioning

confidence: 99%

Rational and semi‐rational solutions of a nonlocal (2 + 1)‐dimensional nonlinear Schrödinger equation

Peng

Tian

Zhang

et al. 2019

Math Methods in App Sciences

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We consider the fully parity-time (PT) symmetric nonlocal (2 + 1)-dimensional nonlinear Schrödinger (NLS) equation with respect to x and y. By using Hirota's bilinear method, we derive the N-soliton solutions of the nonlocal NLS equation. By using the resulting N-soliton solutions and employing long wave limit method, we derive its nonsingular rational solutions and semi-rational solutions. The rational solutions act as the line rogue waves. The semi-rational solutions mean different types of combinations in rogue waves, breathers, and periodic line waves. Furthermore, in order to easily understand the dynamic behaviors of the nonlocal NLS equation, we display some graphics to analyze the characteristics of these solutions. KEYWORDSrational wave, semi-rational wave, soliton wave, the nonlocal (2 + 1)-dimensional NLS equation MSC CLASSIFICATION 35C08; 35Q51; 35Q55Math Meth Appl Sci. 2019;42:6865-6877.wileyonlinelibrary.com/journal/mma

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“…In addition to the NLS equation, it has been known that there exist Kuznetsov‐Ma (KM) soliton, Akhmediev breather (AB), and Peregrine soliton (PS) for the most NLS‐type equations . In recent years, based on Darboux transformation (DT) approach and Hirota's bilinear approach, there have been a number of effects to investigate soliton solutions and rogue wave solutions of nonlinear differential equations . In particular, one of our authors, Wang, investigates the soliton solutions and rogue wave solutions of nonlinear evolution equations(NLEEs).…”

Section: Introductionmentioning

confidence: 99%

“…[16][17][18][19][20][21][22][23][24][25][26][27] In recent years, based on Darboux transformation (DT) approach and Hirota's bilinear approach, there have been a number of effects to investigate soliton solutions and rogue wave solutions of nonlinear differential equations. [28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47] In particular, one of our authors, Wang, [48][49][50][51][52][53][54] investigates the soliton solutions and rogue wave solutions of nonlinear evolution equations (NLEEs).…”

Section: Introductionmentioning

confidence: 99%

Characteristics of rogue waves on a soliton background in a coupled nonlinear Schrödinger equation

Wang

Han

2019

Math Methods in App Sciences

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In this paper, a coupled nonlinear Schrödinger (CNLS) equation, which can describe evolution of localized waves in a two‐mode nonlinear fiber, is under investigation. By using the Darboux‐dressing transformation, the new localized wave solutions of the equation are well constructed with a detailed derivation. These solutions reveal rogue waves on a soliton background. Moreover, the main characteristics of the solutions are discussed with some graphics. Our results would be of much importance in predicting and enriching rogue wave phenomena in nonlinear wave fields.

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Solitary waves, homoclinic breather waves and rogue waves of the (3+1)-dimensional Hirota bilinear equation

Cited by 99 publications

References 46 publications

Solitary Wave and Quasi-Periodic Wave Solutions to a (3+1)-Dimensional Generalized Calogero-Bogoyavlenskii-Schiff Equation

Solitary Wave and Quasi-Periodic Wave Solutions to a (3+1)-Dimensional Generalized Calogero-Bogoyavlenskii-Schiff Equation

Rational and semi‐rational solutions of a nonlocal (2 + 1)‐dimensional nonlinear Schrödinger equation

Characteristics of rogue waves on a soliton background in a coupled nonlinear Schrödinger equation

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