M-lump, high-order breather solutions and interaction dynamics of a generalized $$(2 + 1)$$-dimensional nonlinear wave equation

Zhao, Zhonglong; He, Lingchao

doi:10.1007/s11071-020-05611-9

Cited by 65 publications

(15 citation statements)

References 40 publications

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“…The single lump wave travels black line y = − 1 2 x (black line in Fig. (7)) before the interaction. Then the trajectory of the lump wave changes into line y = − 1 2 x + 294 293 (red line in Fig.…”

Section: N -Soliton Solutionsmentioning

confidence: 99%

“…Then the trajectory of the lump wave changes into line y = − 1 2 x + 294 293 (red line in Fig. (7)) after the interaction. It is notable that the center of the lump wave is located at the bifurcation point of the resonance solitary wave as t = 0.…”

Section: N -Soliton Solutionsmentioning

confidence: 99%

“…The nonlinear localized waves appear in many fields of sciences and technology, such as fluids, Bose-Einstein condensation, shallow waver waves and nonlinear optics. Solitons, lumps, breathers and rogues waves, well known to us, are all the localized waves [1][2][3][4][5][6][7][8][9]. Lump solution is a rational solution localized in all directions in space, which can be seen limit of the infinite period of the breather wave [10][11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

“…( 1) is a generalized model to investigate nonlinear dynamical phenomena in shallow water, plasma and nonlinear optics [49]. We investigated the M -lump, high-order breather and hybrid solutions of the 2DNW equation [50]. Zhao et al studied the integrability and some mixed solutions of Eq.…”

Section: Introductionmentioning

confidence: 99%

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Resonance Y-type soliton, hybrid and quasi-periodic wave solutions of a generalized (2+1)-dimensional nonlinear wave equation

Zhang

Zhao

2021

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In this paper, we consider a generalized (2+1)-dimensional nonlinear wave equation. Based on the bilinear, the N-soliton solutions are obtained. The resonance Y-type soliton and the interaction solutions between M-resonance Y-type solitons and P-resonance Y-type solitons are constructed by adding some new constraints to the parameters of the N-soliton solutions. The new type of two-opening resonance Y-type soliton solutions are presented by choosing some appropriate parameters in 3-soliton solutions. The hybrid solutions consisting of resonance Y-type solitons, breathers and lumps are investigated. The trajectories of the lump waves before and after the collision with the Y-type solitons are analyzed from the perspective of mathematical mechanism. Furthermore, the multi-dimensional Riemann-theta function is employed to investigate the quasi-periodic wave solutions. The one-periodic and two-periodic wave solutions are obtained. The asymptotic properties are systematically analyzed, which establish the relations between the quasi-periodic wave solutions and the soliton solutions. The results may be helpful to provide some effective information to analyze the dynamical behaviors of solitons, fluid mechanics, shallow water waves and optical solitons.

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Section: N -Soliton Solutionsmentioning

confidence: 99%

Section: N -Soliton Solutionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Resonance Y-type soliton, hybrid and quasi-periodic wave solutions of a generalized (2+1)-dimensional nonlinear wave equation

Zhang

Zhao

2021

Preprint

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“…e4k 2 +e5l 2 )(ω 2 +e1k 2 ) .Therefore, from Eqs (32). and(33), we can getu(x, y, t) = 12b tanh[b(kx + ly − ωt)] [b(kx + ly − ωt)].…”

mentioning

confidence: 98%

A New Three Dimensional Dissipative Boussinesq Equation for Rossby Waves and Its Multiple Soliton Solutions☆

Chen

Yang

2021

Preprint

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A new three dimensional nonlinear dynamic theoretical model is derived from fluid mechanics system. In this paper, From the quasi-geostrophic barotropic potential vorticity equation, we obtain a three dimensional dissipative Boussinesq equation by the reduced perturbation method, i.e.utt +e1uxx +e2(u2)xx + e3utxy + e4uxxxx + e5uxxyy = 0. It is emphasized that the new equation is different from the existing Boussinesq equations, which describe the three dimensional nonlinear Rossby waves in the atmosphere. Moreover, we explore the dispersion relation of the linear wave through the new equation. Using the trial function and auxiliary equation method, the two kinds of soliton solutions of the equation are obtained successfully. Finally, the formation mechanism of Rossby waves is discussed by multiple soliton solutions.

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Rogue wave solutions and the bright and dark solitons of the (3+1)-dimensional Jimbo–Miwa equation

2021

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M-lump, high-order breather solutions and interaction dynamics of a generalized $$(2 + 1)$$-dimensional nonlinear wave equation

Cited by 65 publications

References 40 publications

Resonance Y-type soliton, hybrid and quasi-periodic wave solutions of a generalized (2+1)-dimensional nonlinear wave equation

Resonance Y-type soliton, hybrid and quasi-periodic wave solutions of a generalized (2+1)-dimensional nonlinear wave equation

A New Three Dimensional Dissipative Boussinesq Equation for Rossby Waves and Its Multiple Soliton Solutions☆

Rogue wave solutions and the bright and dark solitons of the (3+1)-dimensional Jimbo–Miwa equation

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