Bilinear form, soliton, breather, lump and hybrid solutions for a ($$\varvec{2+1}$$)-dimensional Sawada–Kotera equation

Li, Liu-Qing; Gao, Yi–Tian; Hu, Lei; Jia, Ting-Ting; Ding, Chaoliang; Feng, Yujie

doi:10.1007/s11071-020-05600-y

Cited by 94 publications

(18 citation statements)

References 47 publications

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“…It is found from the graphical outcomes of the breather waves that they are localized in space and time. This is the novel result of the study and the attained breather wave solutions have not yet been reported in other literature [13,15,27,31,32]. The outcomes emanated from the study might be helpful to researchers in understanding the propagation behaviors of the shallow water waves of small amplitude and long wavelength, stratified internal waves in an ocean, and ion-acoustic waves in a plasma.…”

Section: Discussionmentioning

confidence: 72%

“…Equation (1) was proposed by Sawada and Kotera [29] , and also by Caudrey et al [30] independently. According to Liu [27] and Li et al [31] , Eq. (1) has been studied well due to its wide applications in many research fields of science and engineering, such as the gravitational force field, the conformal field, the two-dimensional quantum gravity gauge field, and the long waves in shallow water under gravity.…”

Section: Introductionmentioning

confidence: 99%

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Lump, lump-stripe, and breather wave solutions to the (2 + 1)-dimensional Sawada-Kotera equation in fluid mechanics

Ali

Bilkis²,

Paul

et al. 2021

Heliyon

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The present study investigates the lump, one-stripe, lump-stripe, and breather wave solutions to the (2+1)-dimensional Sawada-Kotera equation using the Hirota bilinear method. For lump and lump-stripe solutions, a quadratic polynomial function, and a quadratic polynomial function in conjunction with an exponential term are assumed for the unknown function f giving the solution to the mentioned equation, respectively. On the other hand, only an exponential function is considered for one-stripe solutions. Besides, the homoclinic test approach is adopted for constructing breather wave solutions. The propagations of the attained lump, lump-stripe, and breather wave solutions are shown through some graphical illustrations. The graphical outputs demonstrate that the lump wave moves along the straight line and exponentially decreases away from the origin of the spatial domain. On the other hand, lump-kink solutions illustrate the fission and fusion interaction behaviors upon the selection of the free parameters. Fission and fusion processes show that the stripe soliton splits into a stripe soliton and a lump soliton, and then the lump soliton merges into one stripe soliton. In addition, the achieved breather waves illustrate the periodic behaviors in the xy -plane. The outcomes of the study can be useful for a better understanding of the physical nature of long waves in shallow water under gravity.

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Section: Discussionmentioning

confidence: 72%

Section: Introductionmentioning

confidence: 99%

Lump, lump-stripe, and breather wave solutions to the (2 + 1)-dimensional Sawada-Kotera equation in fluid mechanics

Ali

Bilkis²,

Paul

et al. 2021

Heliyon

View full text Add to dashboard Cite

show abstract

“…• Via the Hirota-Riemann method, periodic-wave solutions for Eqn. (2), i.e., Solutions (27), have been determined. Figure 3 has displayed the periodic wave.…”

Section: Discussionmentioning

confidence: 99%

“…Solving System (25) leads to Figure 3 shows the propagation of the periodic wave via Solutions (27). Figure 4 displays the periodic waves with the effect of the coefficients α and β: amplitude of the periodic wave increases when the value of α increases to 4, as shown in Fig.…”

Section: Periodic-wave Solutions For Eqn (2)mentioning

confidence: 99%

Bilinear auto-Bäcklund transformation, breather-wave and periodic-wave solutions for a (3+1)-dimensional Boiti–Leon–Manna–Pempinelli equation

et al. 2021

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Incompressible fluids are seen in ocean engineering, biomechanics, astrophysics, etc. A (3+1)-dimensional Boiti-Leon-Manna-Pempinelli equation is hereby investigated. With the help of the Hirota method and symbolic computation, we present a bilinear auto-Bäcklund transformation with some analytic solutions. Based on the existing N -soliton solutions, we determine the higher-order breather solutions, where N is a positive integer. Via the Hirota-Riemann method, we derive the periodic-wave solutions. Graphical representations of the second-order breather and periodic waves are investigated. Moreover, we graphically present the second-order breather and periodic waves with the influence of the coefficients in that equation. Our results might be helpful to understand certain nonlinear phenomena in fluid mechanics.

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“…Relevant soliton issues can be seen in Refs. [15][16][17][18][19][20][21][22][23][24][25][26][27][28]. In the multimode and birefringent fibers, vector optical solitons for the coupled NLS (CNLS) equations have been considered in two (or more) field components with different frequencies or polarizations [29][30][31][32][33][34][35][36][37].…”

Section: Introductionmentioning

confidence: 99%

Vector solitons for the (2 + 1)‐dimensional coupled nonlinear Schrödinger system in the Kerr nonlinear optical fiber

Sun

Tian

et al. 2021

Z Angew Math Mech

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Investigated in this paper is the (2 + 1)-dimensional coupled nonlinear Schrödinger system, which describes the propagation of the optical soliton through the Kerr nonlinear fiber in which each component diffracts in two transverse dimensions. By virtue of the Kadomtsev-Petviashvili hierarchy reduction, we obtain the bright, dark and mixed vector soliton solutions in terms of the Gramian. We investigate the vector solitons graphically: (1) Bright-dark one solitons with one of the components being gray or black are shown. Bouncing, beating, oscillating and breathing effects which appear during the interactions between the bright-dark two solitons are discussed, and those interactions are shape-preserving; (2) Degenerate and non-degenerate dark-dark one solitons are presented. Interaction of the dark-dark two solitons is discussed and the two solitons keep their amplitudes and velocities invariant except for some phase shifts during the interaction; (3) Bound-state and complexes of the bright-bright solitons are presented.

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Bilinear form, soliton, breather, lump and hybrid solutions for a ($$\varvec{2+1}$$)-dimensional Sawada–Kotera equation

Cited by 94 publications

References 47 publications

Lump, lump-stripe, and breather wave solutions to the (2 + 1)-dimensional Sawada-Kotera equation in fluid mechanics

Lump, lump-stripe, and breather wave solutions to the (2 + 1)-dimensional Sawada-Kotera equation in fluid mechanics

Bilinear auto-Bäcklund transformation, breather-wave and periodic-wave solutions for a (3+1)-dimensional Boiti–Leon–Manna–Pempinelli equation

Vector solitons for the (2 + 1)‐dimensional coupled nonlinear Schrödinger system in the Kerr nonlinear optical fiber

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Bilinear form, soliton, breather, lump and hybrid solutions for a ($$\varvec{2+1}$$)-dimensional Sawada–Kotera equation

Cited by 94 publications

References 47 publications

Lump, lump-stripe, and breather wave solutions to the (2 + 1)-dimensional Sawada-Kotera equation in fluid mechanics

Lump, lump-stripe, and breather wave solutions to the (2 + 1)-dimensional Sawada-Kotera equation in fluid mechanics

Bilinear auto-Bäcklund transformation, breather-wave and periodic-wave solutions for a (3+1)-dimensional Boiti–Leon–Manna–Pempinelli equation

Vector solitons for the (2 + 1)‐dimensional coupled nonlinear Schrödinger system in the Kerr nonlinear optical fiber

Contact Info

Product

Resources

About

Lump, lump-stripe, and breather wave solutions to the (2 + 1)-dimensional Sawada-Kotera equation in fluid mechanics

Lump, lump-stripe, and breather wave solutions to the (2 + 1)-dimensional Sawada-Kotera equation in fluid mechanics