Soliton molecules and some novel interaction solutions to the (2+1)-dimensional B-type Kadomtsev–Petviashvili equation

Yang, Xiangyu; Fan, Rong; Li, Biao

doi:10.1088/1402-4896/ab6483

Cited by 65 publications

(30 citation statements)

References 43 publications

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“…Chen-Lee-Liu derivative nonlinear Schrödinger equation (CLL-NLS equation) was firstly put forward by Kundu [5] which is a completely integrable model, and it can be derived from the modified NLS equation which ignores the mean flow term in hydrodynamics [6]. In recent years, many excellent methods have been put forward by the deep study in integrable system, such as Darboux transformation [7,8], Hirota bilinear method [9][10][11], similarity reduction [12], Riemann-Hilbert approach [13][14][15][16][17] and inverse scattering method [18,19]. Among these but not limited to these methods, Zhang et al obtained higher-order solutions of Eq.…”

Section: Introductionmentioning

confidence: 99%

A $$\overline{\partial }$$-dressing method for the mixed Chen–Lee–Liu derivative nonlinear Schrödinger equation

Sun

2022

J Nonlinear Math Phys

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In this work, we apply the $$\overline{\partial }$$ ∂ ¯ -dressing method to study the mixed Chen–Lee–Liu derivative nonlinear Schrödinger equation (CLL–NLS) with non-normalization boundary conditions. The spatial and time spectral problems associate with CLL–NLS equation which are derived from local $$2 \times 2$$ 2 × 2 matrix. A CLL–NLS hierachy with source is proposed by using recursive operator. Based on the $$\overline{\partial }$$ ∂ ¯ -equation, the N-solitons of the CLL–NLS equation are constructed by choosing a special spectral transformation matrix. Further more, the explicit two-soliton is obtained.

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Section: Introductionmentioning

confidence: 99%

A $$\overline{\partial }$$-dressing method for the mixed Chen–Lee–Liu derivative nonlinear Schrödinger equation

Sun

2022

J Nonlinear Math Phys

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“…The soliton solutions can be transformed into breather solutions by introducing mode resonance [7][8][9]. The interaction between soliton molecules and lump molecules can be obtained by combining the Hirota bilinear method with the long-wave limit method [10][11][12].…”

Section: Introductionmentioning

confidence: 99%

Fission and Fusion Solutions to the (2+1)-Dimensional Generalized Konopelchenko–Dubrovsky–Kaup–Kupershmidt Equation Arising in Fluid Mechanics and Plasma Physics

Gao

Deng

2022

Preprint

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Fission and fusion are common phenomena in nature, they usually occur in physical and biological fields. In this paper, we will give new constraint to obtain fission and fusion solutions which have the shape of the letter Y . In combination with velocity resonance method, mode resonance method and long-wave limit method, we construct the interaction solutions of y-type molecules with soliton molecules, breather molecules and lump molecules respectively. We also obtain a novel solution containing a mixture of lump molecules, breather molecules and y-type molecules. At the same time, we analyze the dynamic behaviors of these interaction solutions and give the problems waiting to be solved.

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“…[40] Soliton molecules in conservative systems can be shaped when the group velocities of two or more elementary solitons coincide. [64][65][66][67] In addition to soliton solutions, the nonlinear evolution equations admit large families of breather solutions, [12][13][14][15][16][17][18] which exhibit much more sophisticated dynamics and play a significant role in the formation of rogue waves as well as the development of MI. [30][31][32]68] Consequently, studying the bound states of the breathers is non-negligible.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Wave Molecules for the Lakshmanan–Porsezian–Daniel Equation in Nonlinear Optics and Biology

et al. 2022

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The nonlinear wave molecules of the Lakshmanan–Porsezian–Daniel (LPD) equation describing the propagation of ultrashort optical pulses through optical fibers and Davydov soliton in α‐helical proteins are investigated. Based on the analysis of characteristic lines, the breather molecules consisting of two, three, or even four different breather atoms are derived, and the synthesis modes of molecules by adjusting the values of the phase parameters are generated. The state conversion of the breather molecules is studied and a variety of converted wave molecules are produced. In particular, it is reported that the full conversion of the breather molecules does not exist in the LPD equation. The formation mechanisms of different types of nonlinear wave molecules through the nonlinear superposition are further explored and the influence of higher‐order effects on the breather molecules is discussed. Finally, the intricate interactions between the molecules and nonlinear waves are considered. It is found that the distances between atoms in the molecules as well as the shapes of the converted waves change after the interactions, and the essence of such shape‐changed interactions is revealed.

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Soliton molecules and some novel interaction solutions to the (2+1)-dimensional B-type Kadomtsev–Petviashvili equation

Cited by 65 publications

References 43 publications

A $$\overline{\partial }$$-dressing method for the mixed Chen–Lee–Liu derivative nonlinear Schrödinger equation

A $$\overline{\partial }$$-dressing method for the mixed Chen–Lee–Liu derivative nonlinear Schrödinger equation

Fission and Fusion Solutions to the (2+1)-Dimensional Generalized Konopelchenko–Dubrovsky–Kaup–Kupershmidt Equation Arising in Fluid Mechanics and Plasma Physics

Nonlinear Wave Molecules for the Lakshmanan–Porsezian–Daniel Equation in Nonlinear Optics and Biology

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