Painlevé analysis and new analytic solutions for variable-coefficient Kadomtsev–Petviashvili equation with symbolic computation

Li, Xiaonan; Wei, Guang-Mei; Liang, Yueqian

doi:10.1016/j.amc.2010.05.002

Cited by 12 publications

(8 citation statements)

References 33 publications

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“…where γ is an arbitrary constant. The constraint condition ( 8) is one of the conditions necessary for equation (1) to pass the Painlevé test [15]. We will see that this is a sufficient condition for the GVCKP equation ( 1) to have N -soliton solutions.…”

Section: Single-soliton Solutionsmentioning

confidence: 77%

Variable coefficient equations of the Kadomtsev–Petviashvili hierarchy: multiple soliton solutions and singular multiple soliton solutions

et al. 2012

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We give an introduction to a new direct computational method for constructing multiple soliton solutions to nonlinear equations with variable coefficients in the Kadomtsev–Petviashvili (KP) hierarchy. We discuss in detail how this works for a generalized (3 + 1)-dimensional KP equation with variable coefficients. Explicit soliton, multiple soliton and singular multiple soliton solutions of the equation are obtained under certain constraints on the coefficient functions. Furthermore, the characteristic-line method is applied to discuss the solitonic propagation and collision under the effect of variable coefficients.

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Section: Single-soliton Solutionsmentioning

confidence: 77%

Variable coefficient equations of the Kadomtsev–Petviashvili hierarchy: multiple soliton solutions and singular multiple soliton solutions

et al. 2012

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“…This is important to mention that the above stated condition is totally different from that of the variable coefficient KP equation [9,10].…”

Section: Introductionmentioning

confidence: 93%

“…In addition with these characteristic, the Painlevé test and the existence of conservation laws are also studied. Some relevant information regarding the integrability of KP and variable coefficient KP equation and its Painlevé property is studied detailed in [7]- [10] from which more accurate results about the integrability of the said equation is discussed. Again, in most of the cases, the autonomous NLEEs is considered in past literature whereas, the non-autonomous counter parts are more relevant in the application of real world physical problem.…”

Section: Introductionmentioning

confidence: 99%

Bilinear Backlund, Lax Pairs, Lump waves and Soliton interaction of (2+1)-dimensional non-autonomous Kadomtsev-Petviashvili equation

Roy

Raut²,

Kairi

et al. 2022

Preprint

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This article describes the the characteristic of integrability via Painleve analysis of the Kadomtsev-Petviashvili (KP) equation under the influence of an external force along with a damping. Introducing the Hirota's approach multi-soliton solution of the said equation is acquired in excited systems. Utilizing the obtained solutions, the interaction of solitary wave is observed with special care. It has been observed that Interactive autonomous solitons appear to remain in their original shape after collision. However, the non-autonomous soliton change their shape and directions after collision. The background from which the solitons rises, also significantly changes due to the action of external forces. Further, lump type soliton and some complicated mixed soliton are derived from the bilinear form of the said equation with the appropriate choice of polynomial functions. On the basis of the obtained mixed soliton, the interaction of the strip soliton and lump wave are graphically described. During the investigation of the interaction, fusion type situation is appeared. Finally, from the analytical results of the relevant motions, it is also confirmed that the velocity, maximum altitude and interacting natures of the wave quantities are all influenced by the damping and forcing terms. The interacting natures of the wave quantities are entirely investigated also from numerical understanding.

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“…Several researches focusing on its solutions have emerged including algebraically decaying solutions [3], lump solutions [4], rogue waves [5] and periodic solitons [6]. For more complicated models, such as the ones considered the variation of depth and density, nonautonomous KP equation with variable coefficients should be investigated [7,8] and some researches have been finished [9][10][11][12][13][14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

Periodic parabola solitons for the nonautonomous KP equation

Ma,

Chen,

2018

Preprint

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Kadomtsev-Petviashvili (KP) equation, who can describe different models in fluids and plasmas, has drawn investigation for its solitonic solutions with various methods. In this paper, we focus on the periodic parabola solitons for the (2+1) dimensional nonautonomous KP equations where the necessary constraints of the parameters are figured out. With Painlevé analysis and Hirota bilinear method, we find that the solution has six undetermined parameters as well as analyze the features of some typical cases of the solutions. Based on the constructed solutions, the conditions of their convergence are also discussed.

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Painlevé analysis and new analytic solutions for variable-coefficient Kadomtsev–Petviashvili equation with symbolic computation

Cited by 12 publications

References 33 publications

Variable coefficient equations of the Kadomtsev–Petviashvili hierarchy: multiple soliton solutions and singular multiple soliton solutions

Variable coefficient equations of the Kadomtsev–Petviashvili hierarchy: multiple soliton solutions and singular multiple soliton solutions

Bilinear Backlund, Lax Pairs, Lump waves and Soliton interaction of (2+1)-dimensional non-autonomous Kadomtsev-Petviashvili equation

Periodic parabola solitons for the nonautonomous KP equation

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